help@askiitians.com

+91-87964 74404

Grade 11Modern Physics

Two neutral particles are kept 1 m apart. Suppose by some mechanism some charge is transferred from one particle to the other and the electric potential energy lost is completely converted into a photon. Calculate the longest and the next smaller wavelength of the photon possible.

Simran Bhatia

12 Years agoGrade 11

2 Answers

Navjyot Kalra

12 Years ago

Sol. r = 1 m Energy = kq^2/R = kq^2/1 Now, kQ^2/1 = hc/λ or λ = hc/kq^2 For max ‘λ’, ‘q’ should be min, For λ hc/kq^2 – 0.863 * 10^3 = 863 m. For next smaller wavelength = 6.63 * 3 *10^-34 * 10^8/9 * 10^9 *(1.6 * 2)^2 * 10^-38 = 863/4 = 215.74 m

Dhawal Patil

9 Years ago

As charge is quantized, the least amount of charge that can be transferred is e.

According to the question, energy lost is completely transferred in the form of the photon.

Please note that the energy is lost as conservative forces are considered to be negative if they are attractive in nature.

As electric potential energy =

$-\frac{1}{4\pi\epsilon_o}\!\!\frac{{q}^2}{r}$

And energy of the photon = $h\nu$

We have :

$-\frac{1}{4\pi\epsilon_o}\!\!\frac{{q}^2}{r} = h\nu$

Sustituting, $\nu = \frac{c}{\lambda}$ and discarding the minus sign, we get:

$\frac{1}{4\pi\epsilon_o}\!\!\frac{q^2}{r} = \frac{hc}{\lambda}$

which implies,

$\lambda=\frac{hc}{\frac{1}{4\pi\epsilon_o}\!\!\frac{q^2}{r}}$

Also, $\lambda_{n^{th}largest} = \frac{(6\!\cdot\!63.10^{-34}Js).(3\!\cdot\!0.10^8ms^{-1}).1m)}{(9.10^9Nm^2C^{-2}).(n.1\!\cdot\!6.10^{-19})^2}$

$\therefore\lambda_{largest} = \frac{(6\!\cdot\!63.10^{-34}Js).(3\!\cdot\!0.10^8ms^{-1}).1m)}{(9.10^9Nm^2C^{-2}).(1\!\cdot\!6.10^{-19})^2}$ $\therefore\lambda_{largest} = \frac{(6\!\cdot\!63.10^{-34}Js).(3\!\cdot\!0.10^8ms^{-1}).1m)}{(9.10^9Nm^2C^{-2}).(2.1\!\cdot\!6.10^{-19})^2}=\frac{\lambda_{largest}}{4}$

A particle is projected in vertical plane such that after 5 seconds its velocity becomes horizontal. The maximum height attained by the projectile from point of projection is n3 m. The value of n is _______. (g = 10 m/s2)

modern physics

1 Answer Available

Last Activity: 3 Years ago

Two particles approach each other from very large distance as shown, . if the least separation between the particles is b, what is the speed of M in center of mass frame when particles are closest? (gravity negligible)

modern physics

1 Answer Available

Last Activity: 4 Years ago

Can the sum of two equal vectors be equal to either vector

modern physics

1 Answer Available

Last Activity: 4 Years ago

A nucleus X¹⁸⁴ at rest emitt alpha particle With kinetic energy 9.0MeV. The product Nucleus is Y. The values of Binding energy per nucleon of alpha particle & Y differ by 1.5MeV. The values of Binding energy per nucleon of X & Y differ by (n÷230) MeV, then n is

modern physics

1 Answer Available

Last Activity: 4 Years ago

SUBJECT: PROBLEM BASED ON LINE DETECTION.
Query: How to apply all the filters for line detection on the following piece of image (provided below)? Explain its Observations to comment on its results.

modern physics

1 Answer Available

Last Activity: 4 Years ago

View all Questions