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प्रश्न
An electron in hydrogen atom stays in its second orbit for 10−8 s. How many revolutions will it make around the nucleus at that time?
An electron in hydrogen atom stays in its second orbit for 10−8 s. How many revolutions will it make around the nucleus at that time?
[Given: e = 1.6 × 10-19 C, m = 9.1 × 10-31 kg]
उत्तर
z = 1, m = 9.1 × 10-31 kg, e = 1.6 × 10-19 C,
ε0 = 8.85 × 10-12 C2 / N⋅m2, h = 6.63 × 10-34 J⋅s
n = 2, t = 10-8s
The periodic time of the electron in a hydrogen atom,
T = `(4ε_0^2h^3n^3)/(pime^4)`
= `((4)(8.85 × 10^-12)(6.63 × 10^-34)^3(8))/((3.142)(9.1 × 10^-31)(1.6 × 10^-19)^4)`
= `((4)(8.85)^2(6.63)^3(8))/((3.142)(9.1)(1.6)^4)xx10^-19 s`
= 3.898 × 10-16 s
Let N be the number of revolutions made by the electron in time t. Then, t = NT
∴ N = `t/T`
= `10^-8/(3.898 xx 10^-16)`
= 2.565 × 107
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