According to Bohr atomic model, in which of the following transitions will the frequency be maximum?

Let, n_f, n_i be the final and initial orbit.<br/><br/>As we know that,<br/><br/>$${1 \over \lambda } = 1.09 \times {10^7}\left[ {{1 \over {n_f^2}} - {1 \over {n_i^2}}} \right]$$<br/><br/>Now, checking for each option, we get<br/><br/>(a) $${1 \over \lambda } \propto \left[ {{1 \over {{3^2}}} - {1 \over {{4^2}}}} \right] = \left[ {{1 \over 9} - {1 \over {16}}} \right] = 0.05$$ .... (i)<br/><br/>(b) ${1 \over \lambda } \propto \left[ {{1 \over 1} - {1 \over 4}} \right] = 0.75$ .... (ii)<br/><br/>(c) $${1 \over \lambda } \propto \left[ {{1 \over {16}} - {1 \over {25}}} \right] = 0.0225$$ .... (iii)<br/><br/>(d) ${1 \over \lambda } \propto \left[ {{1 \over 4} - {1 \over 9}} \right] = 0.14$ .... (iv)<br/><br/>The option (b) has highest value.<br/><br/>Since, frequency, $f = {c \over \lambda } \Rightarrow f \propto {1 \over \lambda }$<br/><br/>$\therefore$ Frequency will be maximum for transition n = 2 to n = 1.