The first ionization potential for calcium (Z = 20, A = 40) is 6.11 eV. Singly-ionized calcium (Ca+) produces two very strong absorption lines in the Sun’s spectrum discovered by Joseph Fraunhofer in 1814, who named them "H" and "K" (he didn’t know they were from calcium, as this was >100 years before the development of quantum mechanics). Both lines always appear together, with lambda subscript H equals 3968 end subscript Å and lambda subscript K equals 3933 Å; hence they are called a "doublet
A. What is the speed of an electron that has just barely enough kinetic energy to collisionally ionize a neutral calcium atom? What is the speed of a calcium ion with this same kinetic energy?
B. What is the temperature T of a gas in which the average particle energy is just barely sufficient to ionize a neutral calcium atom?
C. The lower energy level of both lines is the ground state of Cat. What is the difference in energy in eV) between the two states that correspond to the upper energy levels of the Hand Klines, respectively? How does this compare to the energy of a calcium K photon? Can these two lines can be formed by transitions to upper energy levels with different principal quantum numbers (different n), or do they represent transitions with the same n but some different higher-order quantum number? Explain your reasoning based on your understanding of the general behavior of atomic energy levels (En).

Answers

Answer 1

Answer:

A) v = 1.47 10⁶ m / s, v = 0.5426 10⁴ m / s , B)  T = 4.7 10⁴ K, C) n₂ = 42

Explanation:

A)  For this part, let's calculate the speed of an electron that has an energy of 6.11 eV.

Let's reduce the units to the SI system

        E₀ = 6.11eV (1.6 10⁻¹⁹ J / 1eV) = 9.776 10⁻¹⁹ J

The kinetic energy of the electron is

        K = ½ m v²

         E₀ = K

         v = √ 2E₀ / m

         v = √ (2 9.776 10⁻¹⁹ / 9.1 10⁻³¹)

         v = √ (2.14857 10¹²)

         v = 1.47 10⁶ m / s

now the speed of a calcium ion is asked, let's find sum

        m = 40 1.66 10⁻²⁷ = 66.4 10⁻²⁷ kg

         

        v = √ (2E₀ / M)

         v = √ (2 9.776 10⁻¹⁹ / 66.4 10⁻²⁷)

        v = √ (0.2994457 10⁸)

        v = 0.5426 10⁴ m / s

B) the terminal energy of an ideal gas is

             E = 3/2 kT

              T = ⅔ E / k

              T = ⅔ (9,776 10-19 / 1,381 10-23)

              T = 4.7 10⁴ K

C) To calculate the energy of these lines we use the Planck expression

              E = h f

where wavelength and frequency are related

              c =λ f

              f = c /λ

let's substitute

              E = h c /λ

let's look for the energies

λ = 396.8 nm

  E₁ = 6.63 10⁻³⁴ 3 10⁸ / 396.8 10⁻⁹

           E₁ = 5.0126 10⁻¹⁹ J

λ = 393.3 nm

           E₂ = 6.63 10⁻³⁴ 3 10⁸ / 3.93.3 10⁻⁹

           E₂ = 5.0572 10⁻¹⁹ J

The difference in energy between these two states is

          ΔE = E₂ -E₁

          ΔE = (5.0572 - 5.0126) 10⁻¹⁹ J

          ΔE = 0.0446 10⁻¹⁹ J

let's reduce eV

         ΔE = 0.0446 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹ J)

         ΔE = 2.787 10⁻² eV

Now let's use Bohr's atomic model for atoms with one electron,

               E = -13.606 Z² / n²

where 13,606 eV is the energy of the base state of the Hydrogen atom, Z is the atomic number of Calcium

               n = √ (13.606 Z² / E)

λ = 396.8 nm

E₁ = 5.0126 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹J) = 3.132875 eV

               n₁ = √ (13.606 20² / 3.132875)

               n₁ = 41.7

since n must be an integer we take

               n₁ = 42

λ = 393.3 nm

E₂ = 5.0572 10⁻¹⁹ J (1eV / 1.6 10⁻¹⁹ J) = 3.16075 eV

              n₂ = √ (13.606 20² / 3.16075)

              n₂ = 41.5

Again we take n as an integer

               n₂ = 42

We can see that the two lines have the same principal quantum number, so for the difference of these energies there must be other quantum numbers, which are not in the Bohr model, because of the small difference they are possibly due to small numbers of the moment angular orbital or spin


Related Questions

Derivation 1.2 showed how to calculate the work of reversible, isothermal expansion of a perfect gas. Suppose that the expansion is reversible but not isothermal and that the temperature decreases as the expansion proceeds. (a) Find an expression

Answers

Answer:

(a) The work done by the gas on the surroundings is, 17537.016 J

(b) The entropy change of the gas is, 73.0709 J/K

(c) The entropy change of the gas is equal to zero.

Explanation:

(a) The expression used for work done in reversible isothermal expansion will be,

where,

w = work done = ?

n = number of moles of gas  = 4 mole

R = gas constant = 8.314 J/mole K

T = temperature of gas  = 240 K

= initial volume of gas  =  

= final volume of gas  =  

Now put all the given values in the above formula, we get:

The work done by the gas on the surroundings is, 17537.016 J

(b) Now we have to calculate the entropy change of the gas.

As per first law of thermodynamic,

where,

= internal energy

q = heat

w = work done

As we know that, the term internal energy is the depend on the temperature and the process is isothermal that means at constant temperature.

So, at constant temperature the internal energy is equal to zero.

Thus, w = q = 17537.016 J

Formula used for entropy change:

The entropy change of the gas is, 73.0709 J/K

(c) Now we have to calculate the entropy change of the gas when the expansion is reversible and adiabatic instead of isothermal.

As we know that, in adiabatic process there is no heat exchange between the system and surroundings. That means, q = constant = 0

So, from this we conclude that the entropy change of the gas must also be equal to zero.

Explanation:

50 POINTS!!! PLEASE!!!!!! Pls help me with this been stuck on it in like FOREVER!! PLSS.

Answers

Backward. The most force is the 428 g block.

Answer:

it will move in 356.5g in diagonal direction(resultant or between the both direction)

Explanation:

285+428/2=356.5g

Hope u like it

PLZ MARK ME AS BRAINLIEST

I need to write 200 words about: boys are most influenced by their fathers and girls are most influenced by their mothers. Do you agree or disagree?

Answers

Answer:

I agree

Explanation:

I agree because most of the times girls pass more time with their mom since they hace more things in common, it’s the same with the boys.

What would be the speed of an object just before hitting the ground if dropped 100 meters?

Answers

We are given:

the initial height of the object (h) = 100 m

initial velocity (u) = 0 m/s

we will let the value of g = 10 m/s/s

Speed of the object just before hitting the ground:

From the third equation of motion:

v² - u² = 2ah     (where v is the final velocity)

replacing the variables, we get:

v² - (0)² = 2(10)(100)

v² = 2000

v = 10√20 = 44.7 m/s

Therefore, the speed of the object just before hitting the ground is 44.7 m/s

What cause objects to move? In three to five sentences .

Answers

Answer:

Gravity can affect the motion of objects as the force pulls objects closer to earth. Kinetic energy also causes movement in objects as that is energy in motion coming from stored energy known as (potential energy). With almost most importantly is needed is a force as without a force acting upon an objects is moving will continue to move and an object at rest will remain at rest as a gravitational pull or kinetic and potential energy for example are forces.

Explanation:

Have a great day :)

There are 5.5 L of a gas present at -38.0 C. What is the temperature if the volume of the gas has changed to 1.30 L?

Answers

Answer:

We are given:

V1 = 5.5L          T1 = -38 C   or   235 k

V2 = 1.3L           T2 = T

From the gas equation:

PV = nRT

Since the pressure (P) , number of moles (n) and the universal gas constant (R) are constants, we can write the same equation as:

V / T = k  (where k is a constant)

so a bit more insight, since the values noted above are constant, when multiplied by each other, they will provide us with a constant number irrespective of the value of the variables

Changing the variables for the first case:

V1 / T1 = k   (where k is the same constant) ----------------(1)

Similarly,

V2 / T2 = k  (again, k has the same value)----------------(2)

From (1) and (2):

k is the common value

V1 / T1 = V2 / T2

Replacing the variables

5.5 / 235 = 1.3 / T

T = 1.3 * 235 / 5.5

T = 55.54 k

Therefore, at 55.54 K the gas will have a volume of 1.3L

what happens to the temperature of water as time elapses? IF YOU ANSWER IT I WILL MARK YOU A BRAINLEST ANSWER​

Answers

Answer:

I think it will get colder

Explanation:

Answer:

The water molecules go faster as it gets colder they go slower

Explanation:

trust me thats the answer

HELP PLEASE!!!
If we have a sample of silicon (Si) atoms that has 14 protons, 14 electrons, and 18 neutrons
What is the name of this specific silicon isotope?
si-14
si-32
si-46
si-153

Answers

Answer:

It is si-32

Explanation:

Answer:

silicon-32

Explanation:

just took the quiz and got it right

2. Which blood cells help in clotting of the blood​

Answers

Answer:

Platelets

Explanation:

Platelets are tiny blood cells that help your body form clots to stop bleeding. If one of your blood vessels gets damaged, it sends out signals to the platelets. The platelets then rush to the site of damage and form a clot to stop the bleeding.

Answer:

[tex]\boxed {\tt Platelets}[/tex]

Explanation:

There are three main types of blood cells:

Red blood cells: transports oxygen to cells and carbon dioxide to lungsWhite blood cells: protects the body against disease Platelets: help clot blood and stop bleeding

We are looking for which blood cell helps clot the blood. From the list above, we can see the best answer is platelets.

Concerning the work done by a conservative force, which of the following statements, if any, are true? It can always be expressed as the difference between the initial and final values of a potential energy function. It is independent of the path of the body and depends only on the starting and ending points. When the starting and ending points are the same, the total work is zero.

Answers

Answer:

It is independent of the path of the body and depends only on the starting and ending points.

Explanation:

In Physics we define a conservative force as a force that is independent of the path of the body and depends only on the starting and ending points.

For conservative forces we can write;

KEi + PEi = KEf +PEf

where;

KEi= initial kinetic energy

PEi= initial potential energy

KEf= final kinetic energy

PEf= final potential energy

This equation is known as the principle conservation of mechanical energy . It applies only to conservative forces where friction is negligible. The term KE + PE  is also known as the total mechanical energy of the system.

Converting compound units
You would like to know whether silicon will float in mercury and you know that can determine this based on their densities. Unfortunately, you have the density of mercury in units of kilogram/meter3 and the density of silicon in other units: 2.33 gram/centimeter3. You decide to convert the density of silicon into units of kilogram/meter3 to perform the comparison. By which combination of conversion factors will you multiply 2.33 gram/centimeter3 to perform the unit conversion?

Answers

Answer:

Dividing the silicon density by 1000 and then multiply it by 1000000.

Explanation:

A kilogram equals 1000 grams and a cubic meter equals 1000000 cubic centimeters. Hence, we must divide the silicon density by 1000 and then multiply itby 1000000 to convert the value into kilograms per cubic centimeter. That is:

[tex]x = 2.33\,\frac{g}{cm^{3}}\times \frac{1\,kg}{1000\,g}\times \frac{1000000\,cm^{3}}{1\,m^{3}}[/tex]

[tex]x = 2330\,\frac{kg}{m^{3}}[/tex]

In a nutshell, we must multiply the density of silicon by 1000 to obtains its value in kilograms per cubic meter.

The speed of a car is decreasing from 35 m/s to 15 m/s in 4s

Answers

If you are looking for the acceleration
a = -20/4 = -5 m/s^2

A student uses a microwave oven to heat a meal. The wavelength of the radiation is 8.97 cm. What is the energy of one photon of this microwave radiation? Multiply the answer you get by 1025 to be able to input a number more easily into canvas. Enter to 2 decimal places.

Answers

Answer:

The energy of one photon is 2.21x10⁻²⁴ J. Multiplied by 10²⁵ is 22.10 J.

         

Explanation:  

The energy (E) of a photon is:

[tex] E = h\frac{c}{\lambda} [/tex]

Where:

h: is the Planck's constant = 6.62x10⁻³⁴ J.s

λ: is the wavelength of the radiation = 8.97 cm

c: is the speed of light = 3.00x10⁸ m/s

[tex] E = h\frac{c}{\lambda} = 6.62 \cdot 10^{-34} J.s\frac{3.00\cdot 10^{8} m/s}{8.97 \cdot 10^{-2} m} = 2.21 \cdot 10^{-24} J [/tex]

Hence, the energy of one photon is 2.21x10⁻²⁴ J.

Now, if we multiply the answer by 10²⁵ we have:

[tex] E = 2.21 \cdot 10^{-24} J \cdot 10^{25} = 22.10 J [/tex]

I hope it helps you!

The energy of one photon is 2.21x10⁻²⁴ J. Multiplied by 10²⁵ is 22.10 J.

Calculation of energy:

We know that

[tex]E = h\frac{c}{\lambda}[/tex]

Here

h be the Planck's constant = 6.62x10⁻³⁴ J.s

λ be the wavelength of the radiation = 8.97 cm

c be the speed of light = 3.00x10⁸ m/s

Now

Here we need to multiply the answer 10^25 so that the correct answer could come.

[tex]E = 6.62.10^{-34} \frac{3.00.10^{8}}{8.97.10^{-2}}[/tex]

=  2.21x10⁻²⁴ J.

= 22.10 J.

Hence, the energy of one photon is 2.21x10⁻²⁴ J. Multiplied by 10²⁵ is 22.10 J.

learn more about energy here; https://brainly.com/question/24719731

g (a) Calculate the block's final speed when it reaches the bottom of the frictionless inline. Keep 2 decimal places.

Answers

Answer:

Explanation:

The question is incomplete. Here is the complete question with attachment below.

In the above figure on the LEFT side, a block (mass = 2.8 kg) starts from rest at the top of a frictionless inline and slides to the bottom. The height of the incline is h=6.5 m, angle

What is the volume of an object if it has a mass of 10 grams and a density of 87 g/ml

Answers

Answer:

The answer is 0.115 mL

Explanation:

The volume of a substance when given the density and mass can be found by using the formula

[tex]volume = \frac{mass}{density} \\[/tex]

From the question

mass = 10 g

density = 87 g/ml

We have

[tex]volume = \frac{10}{87} \\ = 0.114942528...[/tex]

We have the final answer as

0.115 mL

Hope this helps you

first correct answer gets brainliest

Answers

Answer:

electrical energy transforming into sound energy in speaker

Answer:

the first one. Electrical energy transforming into sound energy in a speaker

how far will a brick starting from rest fall freely in 3.0 seconds?

Answers

Answer: It will be about 44.1m

Explanation:

your answer to this is 44m! hope this helps

Take the regular compass and hold it so the case is vertical. Now use it to investigate the direction of the coil’s magnetic field at locations other than the central axis. What happens as you move away from the center axis toward the coil? What happens above the coil? Outside the coil? Below the coil?

Answers

Answer:

Please find the answer in the explanation

Explanation:

Take the regular compass and hold it so the case is vertical. Now use it to investigate the direction of the coil’s magnetic field at locations other than the central axis.

What happens as you move away from the center axis toward the coil? The direction of the magnetic compass needle will move in an opposite direction since the direction of the induced voltage is reversed.

What happens above the coil?

the needle on the magnetic compass will be deflected. Since compasses work by pointing along magnetic field lines

Outside the coil? The magnetic compass needle will experience no deflection. Since there is no induced voltage or current.

Below the coil?

The needle will move in an opposite direction.

A cup of hot coffee initially at 95 degrees C cools to 80 degrees C in 5 min while sitting in a room of temperature 21 degrees C. Using Newton's law of cooling, determine when the temperature of the coffee will be a nice 50 degrees C.

Answers

Answer:

When the temperature of the coffee is 50 °C, the time will be 20.68 mins

Explanation:

Given;

The initial temperature of the coffee T₀ = 95 °C

The temperature of the room = 21°C

Let T be the temperature at time of cooling t in mins

According to Newton's law of cooling;

[tex]\frac{dT}{dt} \alpha (T-21)\\\\\frac{dT}{dt} = k (T-21)\\\\\frac{dT}{T-21} = kdt\\\\\int\limits {\frac{dT}{T-21}} = \int\limits kdt\\\\Log(T-21) =kt + Logc \\\\Log (\frac{T-21}{c} ) = kt\\\\T -21 = ce^{kt}\\\\At \ t = 0, T = 95\\\\95-21 = ce^0\\\\74 = c\\\\New, equation: T -21 = 74e^{kt}\\\\Again; when \ t= 5\ min, T = 80\\\\80 -21 = 74e^{5k}\\\\59 = 74e^{5k}\\\\e^{5k} = \frac{59}{74}\\\\ 5k = ln(\frac{59}{74})\\\\5k = -0.2265\\\\k = -0.0453[/tex]

When the temperature is 50 °C, the time t in min is calculated as;

[tex]T -21 = 74e^{-0.0453t}\\\\50 -21 = 74e^{-0.0453t}\\\\29 = 74e^{-0.0453t}\\\\\frac{29}{74} = e^{-0.0453t}\\\\0.39189 = e^{-0.0453t}\\\\ln(0.39189 ) = {-0.0453t}\\\\-0.93677 = {-0.0453t}\\\\t = \frac{-0.93677}{-0.0453}\\\\ t = 20.68 \ mins[/tex]

Therefore, when the temperature of the coffee is 50 °C, the time will be 20.68 mins

In 10 minutes the hot coffee will attain the temperature of 50 degrees Celsius.

Initially the hot cup of coffee at the temperature of 95 degrees Celsius but after 5 minutes its temperature decreases from 95 to 85 degrees Celsius which is 15 degrees Celsius decrease so in other 5 minutes, the temperature decreases to 65 degrees Celsius.

Again after 5 minutes the temperature will further decrease finally the cup of coffee attain the temperature of 50 degrees Celsius so we can conclude that in 10 minutes the hot coffee will gain the 50 degrees Celsius temperature.

Learn more: https://brainly.com/question/18402982

A ray is incident at at 50 degrees angle on a plane mirror. What will be the deviation after reflection from the mirror?​

Answers

Answer:

Explanation:

If the ray were not deviated, it would travel straight through the mirror. Due to the mirror, the incident ray is reflected at 30°. The ray travels 30° + 30° = 60°. The angle of deviation is 180° - 60° = 120°.

A man walking at 3.56 m/s accelerates at 2.50 m/s2 for 9.28 s. How far does he get?
141 m
26.8 m
44.6 m
248 m

Answers

This is the answer hope you get it :)

A curve that has a radius of is banked at an angle of . If a -kg car navigates the curve at without skidding, what is the minimum coefficient of static friction between the pavement and the tires

Answers

Answer:

0.65

Explanation:

For whatever reasons, the parameters are not giving. So, I will assume by myself to make the calculations easier. You can substitute whatever it is to it from your question.

Given that

Radius of the road, r = 63 m

Speed of the car, v = 20 m/s

The relationship between a car that is passing through a curve and it's frictional force is said to be

U(s) * g = v²/r

In the formula above,

U(s) = coefficient of static friction

g = acceleration due to gravity, 9.8 m/s²

v = velocity of the car

r = radius of the road

Now when we substitute the earlier stated values, we have

U(s) * 9.8 = 20² / 63

U(s) * 9.8 = 400 / 63

U(s) * 9.8 = 6.35

U(s) = 6.35 / 9.8

U(s) = 0.65

Thus, our coefficient of static friction, based on the stated values is 0.65

An airplane flies with a constant speed of 600 km/h. to the west. How far can it travel in 1/4 hour?

Answers

Answer:

d = 150 km

Explanation:

Speed of an airplane is 600 km/h

We need to find how far it travel in 1/4 hour.

We know that the speed of an object is given by distance travelled divided by the time taken. Let d is the distance covered in 1/4 hour. So,

[tex]v=\dfrac{d}{t}\\\\d=v\times t\\\\d=600\ km/h \times \dfrac{1}{4}\ h\\\\d=150\ km[/tex]

So, it will cover 150 km.

the neuron is considered a (a. Cell. (B.artery. (C. Vein

Answers

Answer:

A Cell

Explanation:

Neurons are considered a cell :)

Write a haiku
poem
explaining
why graphing
is useful.
If you are
able, share
your poem
with others.

Answers

Answer:

Explanation:

graphing is helpful

helps visualize the line

of your equation

Which material could be represented by the image above? (SC.8.P.8.1)
A. Diamonds
B. Milk
C. Oxygen
D. Wood

Answers

Answer:

a. diamonds

Explanation:

solid is the matter that has definite shape and definite volume. One good example is a diamond because contains particles that are strongly attract to each other.

A car takes 8 s to increase its velocity from 10 m/s to
30 m/s. What is its average acceration?

Answers

Answer:

Average acceleration is 2.5 m/s^2.

Explanation:

Average acceleration can be found by dividing the change in speed by the change in time.

We know that the initial velocity=10m/s, the final velocity=30m/s and time elapsed is t=8s.

a= (Final velocity-Initial Velocty)/t

a=(30-10)/8=20/8=2.5 m/s^2

The world’s fastest car can accelerate from rest to 60 mph(27m/s) in 2.2 seconds. What is the magnitude of its acceleration?​

Answers

Hi there! :)

12.27 m/s²

Find the acceleration by finding the change in velocity over time:

(vf - vi) / (time) = acceleration over the interval

*Remember, an object at rest has a velocity of 0 mph, and use the correct units for speed that would result in an acceleration involving meters / seconds.*

(27 - 0) / (2.2) = 27 / 2.2 ≈ 12.27 m/s²

how do you Convert 50 g to kg in an equation for physics

Answers

Answer:

Divide by 1000

Explanation:

whats a difference between a objects kinetic energy and potential energy​

Answers

Answer:

A object having kinetic energy is in motion state.And the object whi posses potential energy i s in state of podition.

Answer:

Objects are relative to other moving and stationary objects.

Kinetic energy can be transferred from one moving object to another.

Potential energy is stored energy in an object.

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