Question

Wave number and frequency of yellow radiation having wavelength $5800\mathring{A}$ are

• A. $1.66 \times 10^{-8} cm ^{-1} ; 7.21 \times 10^{14} s ^{-1}$
• B. $1.92 \times 10^{-4} cm ^{-1} ; 5.172 \times 10^{19} s ^{-1}$
• C. $1.724 \times 10^{4} cm ^{-1} ; 5.172 \times 10^{14} s ^{-1}$
• D. $2.246 \times 10^{4} cm ^{-1} ; 1.72 \times 10^{10} s ^{-1}$

Answer 1

Answer: (C)

$\lambda=5800 \mathring{A}=5800 \times 10^{-8} cm$

$\bar{v}=\frac{1}{\lambda}=\frac{1}{5800 \times 10^{-8}}=\frac{1}{58} \times 10^{6}$

$=\frac{100}{58 \times 10^{-4}}=1.724 \times 10^{4} cm ^{-1}$

$\underset{\text{(frequency)}}{v} =\frac{c}{\lambda}=\frac{3 \times 10^{10} cm / s }{5800 \times 10^{-8} cm }$

$=\frac{30,000}{5800} \times 10^{14}$

$=5.172 \times 10^{14} s ^{-1}$