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
$\Delta E_{1}\to2=-\frac{13.6}{2^{2}}+ \frac{13.6}{1^{2}}=10.2$ eV
$\Delta E_{2}\to3 =- \frac{13.6}{3^{2}}+ \frac{13.6}{2^{2}}=1.9$ eV
$\therefore $ On moving from lower value of $n$ to higher value of $n$ energy difference between successive energy levels decreases.