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### The first three spectral lines of H-atom ....

The first three spectral lines of H-atom in the Balmer series are given by $\lambda_1,\lambda_2,\lambda_3$ respectively. Considering the Bohr atomic model, the ratio of wave lengths of first and third spectral lines $\frac {\lambda_1}{\lambda_3}$ is approximately given by $'x' \times 10^{-1}$.

The value of x, to the nearest integer is-----------.

Solution

$\frac{1}{{{\lambda _1}}} \propto \frac{1}{4} - \frac{1}{9} = \frac{5}{{36}}$

$\frac{1}{{{\lambda _3}}} \propto \frac{1}{4} - \frac{1}{{25}} = \frac{{21}}{{100}}$

$\frac{{{\lambda _1}}}{{{\lambda _3}}} = \frac{{21}}{{100}} \times \frac{{36}}{5} = \frac{{21 \times 9}}{{25 \times 5}} = 15.12 \times {10^{ - 1}}$

$\therefore x = 15$

### Sum of the coefficients in the expansion of $(x+y)^n$ ....

If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$