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Found in: Page 1112

College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

Find the radius of a hydrogen atom in the n = 2 state according to Bohr’s theory.

The radius of a hydrogen atom in the 2nd state is $2.116 \times {10^{ - 10}}\;{\rm{m }}{\rm{.}}$

See the step by step solution

Step 1: Determine the Bohr’s theory

The spectrum of hydrogen atoms is explained by an atomic structure theory. It is assumed that the electron orbiting the nucleus can only exist in particular energy states, with each transition resulting in the emission or absorption of a quantum of radiation.

Step 2: Given information and Formula to be used

Consider the formula for the radius of the atomic orbit is as follows:

${r_B} = \frac{{{n^2}{a_B}}}{z}$

Here, rB is the radius of orbit, n is the energy level, aB is the Bohr's radius and z is the number of proton.

Step 3: Determine the radius of a hydrogen atom in the 2 state.

Radius of hydrogen atom is calculated as

${r_B} = \frac{{{n^2}{a_B}}}{z}$

Substitute the value in the above expression

$\begin{array}{c}{r_B} = \frac{{{{\left( 2 \right)}^2}\left( {0.529 \times {{10}^{ - 10}}\;{\rm{m}}} \right)}}{1}\\{r_B} = {\left( 2 \right)^2}\left( {0.529 \times {{10}^{ - 10}}\;{\rm{m}}} \right)\\{r_B} = 4\left( {0.529 \times {{10}^{ - 10}}\;{\rm{m}}} \right)\\{r_B} = 2.116 \times {10^{ - 10}}\;{\rm{m}}\end{array}$

Hence, the radius of a hydrogen atom in 2 state is $2.116 \times {10^{ - 10}}\;{\rm{m}}$.