We can solve the problem by using the first law of thermodynamics:
where
is the change in internal energy of the system
is the heat absorbed by the system
is the work done by the system on the surrounding
In this problem, the work done by the system is
with a negative sign because the work is done by the surrounding on the system, while the heat absorbed is
with a negative sign as well because it is released by the system.
Therefore, by using the initial equation, we find
1.549×10-19lJ is the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from =7 to =1.
The equation E= hcE =hc, where h is Planck's constant and c is the speed of light, describes the inverse relationship between a photon's energy (E) and the wavelength of light ().
The Rydberg formula is used to determine the energy change.
Rydberg's original formula used wavelengths, but we may rewrite it using units of energy instead. The result is the following.
aaΔE=R(1n2f−1n2i) aa
were
2.17810-18lJ is the Rydberg constant.
The initial and ultimate energy levels are ni and nf.
As a change of pace from
n=5 to n=3 gives us
ΔE
=2.178×10-18lJ (132−152)
=2.178×10-18lJ (19−125)
=2.178×10-18lJ×25 - 9/25×9
=2.178×10-18lJ×16/225
=1.549×10-19lJ
Learn more about Rydberg formula here-
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