The ratio of energies of hydrogen atom in its first excited state to third excited state is

Question

The ratio of energies of hydrogen atom in its first excited state to third excited state is (A) (1/4) (B) (4/1) (C) (3/4) (D) (4/3)

Tardigrade Admin · Accepted Answer

Energy in n text th excited state =(-13.6/(n+1)2) Energy in 1 text st excited state =(-13.6/4) Energy in 3 text ds excited state =(-13.6/16) Ratio E1: E3=4: 1

Q. The ratio of energies of hydrogen atom in its first excited state to third excited state is

$\frac{1}{4}$

$\frac{4}{1}$

$\frac{3}{4}$

$\frac{4}{3}$

Energy in $n^{th}$ excited state $= \frac{- 13.6}{( n + 1 ) ^{2}}$
Energy in $1^{st}$ excited state $= \frac{- 13.6}{4}$
Energy in $3^{ds}$ excited state $= \frac{- 13.6}{16}$
Ratio $E_{1} : E_{3} = 4 : 1$