Which of the following transitions in hydrogen atoms emit photons of highest frequency?

1. Frequency $(\nu )$ is proportional to energy change $(\Delta E)$. Emission occurs when transition is from higher $n$ to lower $n$. This eliminates options A and D.2. The energy levels in Hydrogen are $E_n=-13.6/n^2\text{eV}$.For $n=6$ to $n=2$:
$$\Delta E=13.6\left(\frac{1}{2^2}-\frac{1}{6^2}\right)=13.6\left(\frac{1}{4}-\frac{1}{36}\right)=13.6\times \frac{8}{36}\approx 3.02\text{eV}$$
For $n=2$ to $n=1$:
$$\Delta E=13.6\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=13.6\times \frac{3}{4}=10.2\text{eV}$$
Since $10.2\text{eV}>3.02\text{eV}$, the $n=2\to 1$ transition emits the highest frequency photon.