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In a model of the hydrogen atom, the energy levels Wn are given by the...

Physics
WAEC 2002

In a model of the hydrogen atom, the energy levels Wn are given by the formula Wn = -\(\frac{R}{n^2}\), where n is an integer and R is a constant. Determine the energy released in the transition from n = 3 to n = 2.

  • A. \(\frac{R}{5}\)
  • B. -\(\frac{R}{4}\)
  • C. \(\frac{5R}{36}\)
  • D. \(\frac{-5R}{36}\)
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Correct Answer: Option C
Explanation

Given that W = -\(\frac{R}{n^2}\)

from n = 3 to n = 2.

-\(\frac{R}{3^2}\) - (-\(\frac{R}{2^2}\))

-\(\frac{R}{9}\) - (-\(\frac{R}{4}\))

-\(\frac{R}{9}\) + \(\frac{R}{4}\);

with LCM 36

\(\frac{-4R  + 9R}{36}\)

= \(\frac{5R}{36}\)


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