Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength

2.52    Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength

\\\lambda\ (\textup{nm})\qquad \qquad \qquad 500\quad 450\quad 400\\ \textup{v}\times 10^{-5} \ (\textup{cm s}^{-1})\quad \; 2.55\ \ 4.35\ \ 5.35

Answers (1)

best_answer

Let us assume the threshold wavelength to be \lambda\ nm and the kinetic energy of the radiation is given as:

h(\nu-\nu_{o}) = \frac{1}{2}mv^2

hc\left ( \frac{1}{\lambda} - \frac{1}{\lambda_{o}} \right )= \frac{1}{2}mv^2

\Rightarrow hc\left ( \frac{1}{500\times10^9} - \frac{1}{\lambda\times10^{-9}} \right ) = \frac{1}{2}m\left ( 2.55\times10^5\times10^{-2} \right )^2

\left ( \frac{hc}{10^{-9}} \right )\left ( \frac{1}{500}-\frac{1}{\lambda} \right )= \frac{1}{2}m(2.55\times10^3)^2         .................................(1)

Similarly, we can also write,

\left ( \frac{hc}{10^{-9}} \right )\left ( \frac{1}{450}-\frac{1}{\lambda} \right )= \frac{1}{2}m(3.45\times10^3)^2        ...................................(2)

\left ( \frac{hc}{10^{-9}} \right )\left ( \frac{1}{400}-\frac{1}{\lambda} \right )= \frac{1}{2}m(5.35\times10^3)^2        ...................................(3)

Now, dividing the equations (3) with (1),

\frac{\left ( \frac{\lambda -400}{400\lambda} \right )}{\left (\frac{\lambda -500}{500\lambda} \right )} = \frac{\left ( 5.35\times10^3 \right )^2}{\left ( 2.55\times10^3 \right )^2}

\frac{5\lambda -2000}{4\lambda -2000} = \frac{\left ( 5.35 \right )^2}{\left ( 2.55 \right )^2}

\frac{5\lambda -2000}{4\lambda -2000} = 4.40177

\Rightarrow 17.6070\lambda -5\lambda = 8803.537 -2000

\Rightarrow \lambda = \frac{6805.537}{12.607} = 539.8\ nm

Therefore, the wavelength is 540\ nm.

Posted by

Divya Prakash Singh

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Single Girl Child Scholarship 2024: Registration extended till January 10; eligibility criteria, amount
anam-khan

CBSE wants international boards reined in; letter to education ministry seeks directions for AIU
anam-khan

PM Modi's Pariksha Pe Charcha 2025 to be held next month, registrations open till January 14

Latest Question