Question

calculate the wave number of last line in lyman series in hydrogen spectrum.Given that R=1.09677×10 to the power7 per meter.

Answer 1

As,The last line in Lyman series is At infinity, using the formula (1/Lambda) = R( [1/{n1}^2] - [1/{n2}^2]).

we get 1/(Lambda) or Wave number (Nu) as R

where R is rydberg's constant = 1.09677 × 10^7

Answer 2

Answer: The wave number of last line in lyman series in hydrogen is $0.91\times 10^{7}}m$

Explanation:  

$E=\frac{hc}{\lambda}$

$\lambda$ = Wavelength of radiation

E= energy

For the last line in lyman series, the electron  will jump from first energy level to infinite level.

Using Rydberg's Equation:

$\frac{1}{\lambda}=R_H\left(\frac{1}{n_i^2}-\frac{1}{n_f^2} \right )$

Where,

$\lambda$ = Wavelength of radiation

$\frac{1}{\lambda}=\bar{\nu}$ = wave number

$R_H$ = Rydberg's Constant

$n_f$ = Higher energy level = $\infty$  

$n_i$= Lower energy level = 1 (Lyman series)

Putting the values, in above equation, we get

$\frac{1}{\lambda_{lyman}}=R_H\left(\frac{1}{1^2}-\frac{1}{\infty^2} \right )$

$\frac{1}{\lambda_{lyman}}=\frac{1}{1.09677\tiimes 10^{-7}}$

$\bar{\nu}=0.91\times 10^{7}}m$