Question 500: Atoms & Nuclei

Question

The radius of inner most orbit of hydrogen atom is $5.3 	imes 10^{-11} \mathrm{~m}$. What is the radius of third allowed orbit of hydrogen atom?

Accepted Answer

The formula to calculate the radius of the nth orbit in a hydrogen atom is given by the equation:
$r_n = r_0 	imes n^2$
where,
$r_n$ is the radius of the nth orbit,
$r_0$ is the radius of the innermost orbit (known as the Bohr radius), and
$n$ is the orbit number.
Given that the radius of the innermost orbit ($r_0$) is $5.3 	imes 10^{-11} \mathrm{~m}$ or equivalently $0.53 \mathop A\limits^o$, and we're interested in finding the radius of the third orbit ($n = 3$).
So,
$r_3 = 0.53 	imes (3)^2$ $\mathop A\limits^o$
$r_3 = 0.53 	imes 9$ $\mathop A\limits^o$
$r_3 = 4.77$ $\mathop A\limits^o$
Therefore, the radius of the third allowed orbit of the hydrogen atom is
4.77
$\mathop A\limits^o$.

Answer

1.06 $\mathop A\limits^o $

Answer

1.59 $\mathop A\limits^o $

Answer

4.77 $\mathop A\limits^o $

Answer

0.53 $\mathop A\limits^o $

Atoms & Nuclei

The radius of inner most orbit of hydrogen atom is 5.3 \times 10^{-11} \mathrm{~m}. What is the radius of third allowed orbit of hydrogen atom?

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