energy levels of hydrogen atom

Classical Mechanics Level 2

The above is a schematic diagram of the energy levels of a hydrogen atom, where $\lambda_1$ and $\lambda_2$ are the wavelengths of the electromagnetic waves released when the electron transition from $n=4$ to $n=3,$ or from $n=4$ to $n=1,$ occurs. Which of the following statements is correct?

a) The wavelength $\lambda_1$ is longer than the wavelength $\lambda_2$ .

b) The electromagnetic wave released when the electron transition from $n=4$ to $n=3$ occurs is a visible light.

c) The electron at $n=4$ releases more energy when it transits to $n=3$ than when it transits to $n=1$ .

a) and c) a) only b) only c) only

1 solution

Andre Yudhistika
Feb 26, 2014

energy is equal to n1-n2 so E1=4-3=1 E2=4-1=3 therefore E2>E1 the greater the energy,the shorter the wave length therefore lambda1>lambda2

Here's another solution to the problem

Energy at a specific level n is -13.6/n^2. For calculating energy change during the process of transition, we apply -13.6/nf^2 +13.6/ni^2 where nf is the final energy level( the energy level after transition) and ni is the initial energy level before transition. In one case E=-13.6/1^2+13.6/4^2 In the other case E=-13.6/3^2+13.6/4^2 In the latter case the energy will be greater..and since E=hf ;the greater the energy the lesser will be lambda (wavelength).

Ifrah Idrees - 7 years ago

energy levels of hydrogen atom

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