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Atoms — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsAtoms3 Marks
Question
  1. Using Bohr's second postulate of quantization of orbital angular momentum show that the circumference of the electron in the nth orbital state in hydrogen atom is n times the de Broglie wavelength associated with it.
  2. The electron in hydrogen atom is initially in the third excited state.What is the maximum number of spectral lines which can be emitted when it finally moves to the ground state?
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Answer

  1. According to Bohr's second postulate

$\text{mvr}_{n} =\frac{\text{nh}}{2\pi}$

$\Rightarrow2\pi\text{r}_{n} = \frac{\text{nh}}{\text{mv}}$

But $\frac{\text{h}}{\text{mv}} =\frac{\text{h}}{\text{p}} =\lambda$

$\therefore2\pi\text{r}_{n} = \text{n}\lambda$

  1. For third excited state n = 4

for ground state n = 1

Hence possible transitions are

n1 = 4 to n1 = 3, 2, 1
n1 = 3 to n1 = 2, 1
n1 = 2 to n1 = 1

Total number of transitions = 6

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