Question

Which statement is true?

• A. Spacing between energy levels $n=1$ and $n=2$ in hydrogen atom is greater than that of $n=2$ and $n=3$
• B. Spacing between energy levels $n=1$ and $n=2$ in hydrogen atom is equal to that $n-2$ and $n=3$
• C. Spacing between energy levels $n=1$ and $n=3$ in hydrogen atom is less than that of $n=2$ and $n=3$
• D. None

Answer 1

Answer: (A)

$E_n=-\frac{13.6Z^2}{n^2}$eV
$\Delta E_1\to 2=-\frac{13.6}{2^2}+\frac{13.6}{1^2}=10.2$ eV
$\Delta E_2\to 3=-\frac{13.6}{3^2}+\frac{13.6}{2^2}=1.9$ eV
$\therefore$ On moving from lower value of $n$ to higher value of $n$ energy difference between successive energy levels decreases.