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Wave Optics

Question

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The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10^–11 m. What are the radii of the n = 2 and n = 3 orbits?

Solution

Given,
$Radius of the innermost electron orbit, r_{0} = 5.3 \times 10^{- 11} m$

As oper the formula of radius of orbit, $r = r_{0} . n^{2}$

(i) When, $n = 2$

Radius, r = $5.3 \times 10^{- 11} \times (2)^{2}$

$r = 21.2 \times 10^{- 11} m = 2.12 \times 10^{- 10} m$

(ii) When $n = 3$

We have,

Radius, r = $5.3 \times 10^{^{- 11}} m \times (3)^{2}$
$= 47.7 \times 10^{- 11} m = 4.77 \times 10^{- 10} m .$

Some More Questions From Wave Optics Chapter

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
Is the probability of backward scattering (i.e., scattering of α-particles at angles greater than 90°) predicted by Thomson's model much less, about the same, or much greater than that predicted by Rutherford's model?

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
Keeping other factors fixed, it is found experimentally that for small thickness t, the number of α-particles scattered at moderate angles is proportional to t. What clue does this linear dependence on t provide?

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