Question

The frequency of revolution of an electron in $nth$ orbit is $f_n$. If the electron makes a transition from the $nth$ orbit to $(n-1)th$ orbit, then the relation between the frequency $\left(v\right)$ of emitted photon and $f_n$ will be :

• A. $v=f_n^2$
• B. $v=\sqrt{f_n}$
• C. $v=\frac{1}{f_n}$
• D. $v=f_n$

Answer 1

Answer: (D)

$v=f_n$

f= mZ²e^4/4n³h³ϵ₀²

f(n-1)=fn.(n/n-1)^3

and

E=-mZ²e⁴/8ε₀²h²n²

so, E=-fhn/2

now for transition within n to (n-1)

hv=f(n).h.n/2-f(n-1).h.n/2

v=f(n)/2{[n^4-(n-1)^4]/n^3}

so v=Kf(n)

v proportional to f(n) but some of its multiple