Question 417: Atoms & Nuclei

Question

The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is

Accepted Answer

The radius of the $ n $-th Bohr orbit for an electron in a hydrogen atom is given by:
$$ r_n = n^2 \cdot r_1 $$
where $ r_1 $ is the radius of the first Bohr orbit (also known as the Bohr radius).
For the first orbit ($ n = 1 $):
$$ r_1 = 1^2 \cdot r_1 = r_1 $$
For the second orbit ($ n = 2 $):
$$ r_2 = 2^2 \cdot r_1 = 4r_1 $$
The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit is:
$$ \frac{r_1}{r_2} = \frac{r_1}{4r_1} = \frac{1}{4} $$
Thus, the correct answer is:
Option C
$$1: 4$$

Answer

$4: 1$

Answer

$2: 1$

Answer

$1: 4$

Answer

$1: 2$

Atoms & Nuclei

The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is

Choose the correct answer: