First slide

Bohr's atom model

Question

In hydrogen and hydrogen-like atoms, the ratio of $E_{4 n} - E_{2 n}$ and $E_{2 n} - E_{n}$ varies with atomic number z and principal quantum number n as

Moderate

A

$\frac{z^{2}}{n^{2}}$
B

$\frac{z^{4}}{n^{4}}$
C

$\frac{z}{n}$
D

$\frac{1}{4}$

Solution

$\frac{E_{4 n} - E_{2 n}}{E_{2 n} - E_{n}} = \frac{\frac{E_{1}}{16 n^{2}} - \frac{E_{1}}{4 n^{2}}}{\frac{E_{1}}{4 n^{2}} - \frac{E_{1}}{n^{2}}} = \frac{1}{4} = constant$

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