Question

the velocity in third orbit of h atom is V cm/s then number of revolutions per secondd around the nucleus in this orbit is given by:
1] 3 . 10*-7
2}137v
3] V/30
4]V/ 3 . 10*-7

Answer 1

Your answer:

Radius of 3rd orbit = 3² × 0.529 × 10⁻⁸ = 4.761 × 10⁻⁸

mvr = $\frac{nh}{2\pi}$

v = $\frac{nh}{2\pi mr}$

n = 3

h = 6.624 × 10⁻²⁷

m = 9.1 × 10⁻²⁸ g

r = 4.761 × 10⁻⁸

Substituting all the values in the formula v = $\frac{nh}{2\pi mr}$

v = $\frac{3\times6.624\times10^-^2^7}{2\times3.14\times9.1\times10^-^2^8\times4.761\times10^-^8}$ = 0.729 × 10⁸ cm/s

No. of revolutions per second =  $\frac{v}{2\pi r}$

= $\frac{0.729\times10^8}{4.761\times10^-^8\times2\times3.14}$ = 2.43 × 10¹⁴ rev/sec

When you take the relation between the revolutions and velocity, you will get the relation as:

$\frac{0.729\times10^8}{2.43 \times 10^1^4}$ = 3 × 10⁻⁷

So, option a is the answer

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