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Determine the final end (final) value of n in a hydrogen atom transition, if electron starts in n = 1 and the atom absorbs a photon of light with an energy of 2.044 X 10^-18J?
thank you very much for your help
Determine the final end (final) value of n in a hydrogen atom transition, if electron starts in n = 1 and the atom absorbs a photon of light with an energy of 2.044 X 10^-18J?
Here's the solution :)
1/wavelength= Rh(1/n1^2-1/n2^2)
speed of light = wavelength X frequency
wavelength= speed/frequency
Rh = 1.09678 X 10^7 (M-1)
Energy = H X V
2.044 X 10^-18 = 6.626 X 10^-34 X V
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V= 3.085 X 10^15
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1/wavelength =1.09678 X 10^7 (1-1/n2^2)
1/speed/frequency = RH ( 1- 1/n2^2)
frequency/Speed X RH = (1-1/n2^2)
3.085 X 10^15 / 3 X 10^8 X 1.09687 X 10^7 =(1-1/n2^2)
3.085 X 10^15 X 10^-8 X 10 ^-7 / 3 X 1.09678 = (1- 1/n2^2)
0.938 = (1- 1/n2^2)
1/n2^2 = 1-0.938 = 0.062
n2^2 = 1/0.062 = 16
n = 4
you welcome
1/wavelength = 1.9678 X 10^7 m^-1 (1/1-1/n^2)
1/9.68 X 10^-8 = 1.09678 X 10^7 m^-1(1-1/n^2)
Is this right , how to solve the rest ?
Oh, you're asking me to do some calculations? I'm more of a clown than a mathematician, but let me give it a try!
We can use the formula for the energy of a photon: E = -13.6 eV / n², where E is the energy in electron volts and n is the initial energy level.
First, let's convert the energy of the photon from joules to electron volts. We know that 1 eV is equal to 1.602 x 10^-19 J, so:
Energy of the photon = 2.044 x 10^-18 J * (1 eV / 1.602 x 10^-19 J)
= 12.75 eV
Now, we can rearrange the formula to solve for n:
E = -13.6 eV / n²
Rearranging it further:
n² = -13.6 eV / E
Plugging in the values we have:
n² = -13.6 eV / 12.75 eV
n² = 1.0667
Taking the square root of both sides:
n = √(1.0667)
n ≈ 1.033
There you have it! The final value of n in the hydrogen atom transition would be approximately 1.033. Just keep in mind that my calculations might be a bit silly, so it's always good to double-check with a more serious source.
To determine the final end value of n in a hydrogen atom transition, we can use the formula for the energy of a photon absorbed or emitted during a transition in the hydrogen atom:
E = 13.6 * (1/n²) - 13.6 * (1/n'²)
where E is the energy of the photon, n is the initial value of n, and n' is the final value of n.
In this case, we have an energy of 2.044 × 10^-18 J and the electron starts in n = 1. We need to solve the equation for n' using this known information.
2.044 × 10^-18 J = 13.6 * (1/1²) - 13.6 * (1/n'²)
Simplifying the equation, we get:
2.044 × 10^-18 J = 13.6 - 13.6 * (1/n'²)
Rearranging the equation, we have:
13.6 * (1/n'²) = 13.6 - 2.044 × 10^-18 J
Dividing both sides by 13.6:
1/n'² = 1 - (2.044 × 10^-18 J) / 13.6
Calculating the right side:
1/n'² ≈ 1 - 0.00000000000015
1/n'² ≈ 0.99999999999985
To find the value of n', we take the square root of both sides:
1/n' = √(0.99999999999985)
Taking the reciprocal of both sides:
n' = 1 / √(0.99999999999985)
Calculating the right side:
n' ≈ 1 / 0.99999999999993
n' ≈ 1
Therefore, the final end value of n in the hydrogen atom transition is n = 1.