WBJEE 2024 Physics & Chemistry Paper

In the Bohr model, the velocity of an electron in an orbit is inversely proportional to the radius of that orbit for a given atom or ion. Specifically, the velocity v of an electron in the nth orbit of a hydrogenlike atom (or ion) is given by:
vn=‌

k

n

Where k is a constant for a particular atom/ion and n is the principal quantum number of the orbit ( 1 for the first orbit, 2 for the second, etc.).
From this relationship, it follows that the velocity of the electron decreases as the principal quantum number increases. Specifically, for the electron in the first Bohr orbit (n=1) and the third Bohr orbit (n=3) of the He+ ion, the velocities v1 and v3 would be directly related by the ratio of their orbit numbers. Thus:
‌

v3

v1

=‌

‌ k 3

k 1

=‌

1

3

Therefore, the velocity ratio v3:v1 is 1:3. This indicates that the electron in the third orbit moves at one-third the velocity of the electron in the first orbit.
Hence, the correct answer is Option C: 1:3.