In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n - 1). If n 1, the frequency of radiation emitted is proportional to

Question

In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n - 1). If n > > 1, the frequency of radiation emitted is proportional to (A) (1/n3) (B) (1/n) (C) (1/n2) (D) (1/n3/2)

Tardigrade Admin · Accepted Answer

In a hydrogen like atom, when an electron makes an transition from an energy level with n to n - 1, the frequency of emitted radiation is

υ = R c Z^{2} [\frac{1}{( n - 1 ) ^{2}} - \frac{1}{n ^{2}}] = \frac{R c Z ^{2} ( 2 n - 1 )}{n ^{2} ( n - 1 ) ^{2}}

As n > > 1

∴ υ = \frac{R c Z ^{2} 2 N}{n ^{4}} = \frac{2 R c Z ^{2}}{n ^{3}}

or

υ \propto \frac{1}{n ^{3}}

Q. In a hydrogen like atom electron makes transition from an energy level with quantum number $n$ to another with quantum number $(n - 1) . I f n >> 1$ , the frequency of radiation emitted is proportional to

$\frac{1}{n ^{3}}$

$\frac{1}{n}$

$\frac{1}{n ^{2}}$

$\frac{1}{n ^{3/2}}$

Q. In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n−1).Ifn>>1, the frequency of radiation emitted is proportional to

n31​

n1​

n21​

n3/21​

In a hydrogen like atom, when an electron makes an transition from an energy level with n to n - 1, the frequency of emitted radiation is υ=RcZ2[(n−1)21​−n21​]=n2(n−1)2RcZ2(2n−1)​ As n > > 1 ∴υ=n4RcZ22N​=n32RcZ2​ or υ∝n31​

Q. In a hydrogen like atom electron makes transition from an energy level with quantum number $n$ to another with quantum number $(n - 1) . I f n >> 1$ , the frequency of radiation emitted is proportional to

$\frac{1}{n ^{3}}$

$\frac{1}{n}$

$\frac{1}{n ^{2}}$

$\frac{1}{n ^{3/2}}$