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Question: According to Bohr’s theory, the wave number of last line of Balmer series is \[(\text{Given }R = 1....

According to Bohr’s theory, the wave number of last line of Balmer series is

(Given R=1.1×107m−1)(\text{Given }R = 1.1 \times 10^{7}m^{- 1})

A

5.5×105m−15.5 \times 10^{5}m^{- 1}

B

4.4×107m−14.4 \times 10^{7}m^{- 1}

C

2.75×106m−12.75 \times 10^{6}m^{- 1}

D

2.75×108m−12.75 \times 10^{8}m^{- 1}

Answer

2.75×106m−12.75 \times 10^{6}m^{- 1}

Explanation

Solution

For last line of Balmer series n1=2n_{1} = 2 and n2=∞n_{2} = \infty

1λ=R[1n12−1n22]=1.1×1074m−1=2.75×106m−1\frac{1}{\lambda} = R\left\lbrack \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right\rbrack = \frac{1.1 \times 10^{7}}{4}m^{- 1} = 2.75 \times 10^{6}m^{- 1}