Question

According to Bohr's hydrogen model, Which of the following is a allowed value of radius of the atom? (given Bohr radius is \(r_0=0.529\times 10^{-10}\,m\))
1. 1 × 10-11 m
2. 2.116 × 10^-12 m
3. 0.529 × 10-15 m
4. 2.116 × 10-10 m

Answer 1

Correct Answer - Option 4 : 2.116 × 10-10 m

CONCEPT:

• Bohr’s proposed that electrons orbited the nucleus in specific orbits or shells with a fixed radius.
• Mathematically, the allowed value of the atomic radius is given by the equation:

\(r_n=n^2\times r_0\)

Where n is a positive integer, r₀ is the smallest allowed radius for the hydrogen atom also known as Bohr’s radius.

CALCULATION:

Given that \(r_0=0.529\times 10^{-10}\,m\)

\(r_n=n^2\times 0.529\times 10^{-10}\,m\)

put n = 1

\(r_1=1^2\times 0.529\times 10^{-10}\,m=​​0.529\times 10^{-10}\,m\)

Similarly put n = 2, 3, 4 .........

\(r_2=2^2\times 0.529\times 10^{-10}\,m=​​2.116\times 10^{-10}\,m\)

\(r_3=3^2\times 0.529\times 10^{-10}\,m=4.761\times 10^{-10}\,m\)

we can get different values.

The minimum value of r for n = 1, will be

\(r_1=​​0.529\times 10^{-10}\,m\)

In the options other than option 4, all the values are less than the minimum value of radius.

However, putting n = 2 we are getting radius \(r_2=2.116\times 10^{-10}\,m\) i.e. option 4.

Hence the correct answer is option 4.