Modern Physics

The angular momentum for hydrogen atom is given by: From Bohr's quantization condition: In this question, we are given: Since and for hydrogen-like atoms and , we can also say: Let’s use the definition , and from Bohr’s model , and since , then: Hence, Now, since the angular momenta are in the ratio:

The momentum of the electron changes due to the electric field: Since , the momentum becomes: Using de Broglie’s relation:

4 days = 96 hours. Half-life hours. So, number of half-lives: Remaining fraction =
Fraction decayed =

The radius of a nucleus is given by , where is the mass number and is a constant.
For , .
For , .
Ratio .

Line-of-sight and satellite communication require direct propagation of waves without reflection or diffraction around obstacles.
Space waves travel in a straight line and are used for such communications (e.g., FM radio, TV, satellite).
Ground waves follow the Earth’s surface, sky waves reflect off the ionosphere, and surface waves are not a standard term in this context.

Energy difference for hydrogen-like atoms is: For Li : , transition from 3 to 2 For He : , transition from 4 to 1 So,