Emission & Energy levels of Hydrogen Problem

In summary, the transition that gives rise to the emission of a 388-nm photon from hydrogen gas involves values of n ranging from n=8 to n=2, according to the Rydberg formula. This formula states that the reciprocal of the wavelength is equal to the Rydberg constant multiplied by the difference between the reciprocal of the initial energy level (n_1) and the reciprocal of the final energy level (n_2), where n_1 is less than n_2. In this case, n_1=8 and n_2=2.
  • #1
crimsondarkn
13
0

Homework Statement



What values of n are involved in the transition that gives the rise to the emission of a 388-nm photon from hydrogen gas?


Homework Equations



n=?
wavelength = 388nm=3.88x10^-7 m
R=1.097x10^7 m^-1

E= hc/ wavelength


The Attempt at a Solution



E= hc/ wavelength=(6.63x10^-34)(3.00x10^8)/ (3.88x10^-7) = 5.13x10^-19 J = 3.206 eV

En = -13.6eV / n^2
n = - square root of (13.6/En) = -square root of (13.6/3.206) = - square root of 4.24 = -2.06

n = 2 <- 1st excited state


the answer is n=8 to n= 2.

How would I know that it began from n=8 ?? Maybe there's an equation that I missed..
 
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  • #2
The formula you need to know for this is the rydberg formula.

[tex]\frac{1}{\lambda}=R_H \left(\frac{1}{(n_1)^2}-\frac{1}{(n_2)^2}\right)[/tex] where, [tex]n_1<n_2[/tex]
 
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  • #3



The emission of a 388-nm photon from hydrogen gas involves a transition from the n=8 energy level to the n=2 energy level. This can be determined by using the Rydberg formula, which relates the energy levels of hydrogen to the wavelength of the emitted photon. In this case, we know the wavelength (388 nm) and the Rydberg constant (1.097x10^7 m^-1), so we can rearrange the formula to solve for the initial energy level (n):

1/lambda = R(1/n_final^2 - 1/n_initial^2)

1/3.88x10^-7 = 1.097x10^7 (1/2^2 - 1/n_initial^2)

n_initial = sqrt(1/1.097x10^7 - 4) = sqrt(0.091) = 0.302

Since n must be a positive integer, the only possible value for n_initial is 1, which corresponds to the ground state of hydrogen. Therefore, the transition must have started from n=8 (final energy level) to n=1 (initial energy level), and then from n=1 to n=2. This is known as the Balmer series in the hydrogen emission spectrum.

In summary, the emission of a 388-nm photon from hydrogen gas involves a transition from the n=8 energy level to the n=2 energy level, which can be determined by using the Rydberg formula and considering the possible energy levels of hydrogen.
 

1. What is the main cause of hydrogen emissions and energy levels?

The main cause of hydrogen emissions and energy levels is the process of combustion, where hydrogen reacts with oxygen to produce energy in the form of heat and water vapor.

2. How does the emission of hydrogen compare to other fossil fuels?

Hydrogen emissions are much lower than other fossil fuels, such as coal and oil. When combusted, hydrogen only produces water vapor, making it a clean source of energy.

3. Can hydrogen be used as a renewable source of energy?

Yes, hydrogen can be produced through renewable sources, such as electrolysis of water using renewable electricity. This makes it a sustainable and environmentally friendly source of energy.

4. What are the potential benefits of using hydrogen as an energy source?

There are several potential benefits of using hydrogen as an energy source, including reduced greenhouse gas emissions, improved air quality, and increased energy independence.

5. What are the challenges in implementing hydrogen as a mainstream energy source?

Some challenges in implementing hydrogen as a mainstream energy source include high production costs, limited infrastructure for distribution and storage, and the need for further technological advancements for efficient utilization.

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