Use Bohr model speed relation

For the hydrogen atom, the speed of electron in the $n^{\text{th}}$ orbit is $v_n \propto \frac{1}{n}$ More specifically, $v_n = \frac{v_1}{n}$

Relate speeds in 7th and 3rd orbits

Therefore, $\frac{v_3}{v_7} = \frac{7}{3}$

Given: $v_7 = 3.6 \times 10^6\ \text{m/s}$

So, $v_3 = v_7 \cdot \frac{7}{3}$

Calculate

$v_3 = 3.6 \times 10^6 \times \frac{7}{3}$

$v_3 = 1.2 \times 7 \times 10^6$

$v_3 = 8.4 \times 10^6\ \text{m/s}$

Match with options

$8.4 \times 10^6\ \text{m/s}$ corresponds to Option C.

Comparison with stored answer

Stored correct answer: C

Derived answer: C

Hence, the derived answer agrees with the stored answer.