Use power of a light source

Power emitted in terms of photons is $P = n \cdot \frac{hc}{\lambda}$ where:

• $n$ = number of photons emitted per second
• $\frac{hc}{\lambda}$ = energy of one photon

Given data

For source $S_1$: $n_1 = 2 \times 10^{15}\ \text{photons/s}, \qquad \lambda_1 = 600\ \text{nm}$

For source $S_2$: $\lambda_2 = 300\ \text{nm}$

Also, $\frac{P_1}{P_2} = 2$

Write powers of both sources

$P_1 = n_1 \frac{hc}{\lambda_1}, \qquad P_2 = n_2 \frac{hc}{\lambda_2}$

Therefore, $\frac{P_1}{P_2} = \frac{n_1 \frac{hc}{\lambda_1}}{n_2 \frac{hc}{\lambda_2}} = \frac{n_1 \lambda_2}{n_2 \lambda_1}$

Substitute the ratio

$2 = \frac{n_1 \lambda_2}{n_2 \lambda_1}$

$2 = \frac{(2 \times 10^{15})(300)}{n_2(600)}$

$2 = \frac{2 \times 10^{15} \times 1}{2n_2} = \frac{10^{15}}{n_2}$

So, $n_2 = \frac{10^{15}}{2} = 5 \times 10^{14}$

Final answer

The number of photons emitted per second by $S_2$ is $5 \times 10^{14}$

Hence, the required integer is: $\boxed{5}$