Question 466: Atoms & Nuclei

Question

The radius of innermost orbit of hydrogen atom is $5.3 	imes 10^{-11} \mathrm{~m}$. The radius of fourth allowed orbit of hydrogen atom is

Accepted Answer

The radius of the orbit in a hydrogen atom is determined by the formula for the Bohr model of the hydrogen atom. The radius of the $ n $-th orbit is given by:
$$ r_n = n^2 	imes r_1 $$
where $ r_1 $ is the radius of the innermost orbit (ground state, $ n=1 $) and $ n $ is the principal quantum number.
Given:
The radius of the innermost orbit (ground state) is $ r_1 = 5.3 	imes 10^{-11} \, 	ext{m} $.
For the fourth orbit ($ n = 4 $), the radius is calculated as follows:
$$ r_4 = 4^2 	imes r_1 = 16 	imes 5.3 	imes 10^{-11} \, 	ext{m} $$
Calculate $ r_4 $:
$$ r_4 = 16 	imes 5.3 	imes 10^{-11} = 84.8 	imes 10^{-11} \, 	ext{m} $$
Converting meters to ÃÂ¥ngstrÃÂ¶ms (where $ 1 \, 	ext{ÃÂ} = 10^{-10} \, 	ext{m} $):
$$ r_4 = 8.48 \, 	ext{ÃÂ} $$
Therefore, the radius of the fourth allowed orbit of the hydrogen atom is:
Option A
8.48 $$\mathop A\limits^o $$

Answer

8.48 $$\mathop A\limits^o $$

Answer

2.12 $$\mathop A\limits^o $$

Answer

4.77 $$\mathop A\limits^o $$

Answer

0.53 $$\mathop A\limits^o $$

Atoms & Nuclei

The radius of innermost orbit of hydrogen atom is 5.3 \times 10^{-11} \mathrm{~m}. The radius of fourth allowed orbit of hydrogen atom is

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