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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