A moving proton and electron have the same de-Broglie wavelength. If K and P denote the K.E. and momentum respectively. Then choose the correct option :
A
Kp < Ke and Pp = Pe
B
Kp = Ke and Pp = Pe
C
Kp < Ke an Pp < Pe
D
Kp > Ke and Pp = Pe
Explanation
$${\lambda _p} = {h \over {{P_p}}}$$
$${\lambda _e} = {h \over {{P_e}}}$$
$$\because$$ $${\lambda _p} = {\lambda _e}$$
$$ \Rightarrow {P_p} = {P_e}$$
$${(K)_p} = {{P_p^2} \over {2{m_p}}}$$
$${(K)_e} = {{P_e^2} \over {2{m_e}}}$$
Kp < Ke as mp > me
Option (a)
2
JEE Main 2021 (Online) 31st August Morning Shift
MCQ (Single Correct Answer)
A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B versus time is :
(Assume that at t = 0, there are no B atoms in the sample)
A
B
C
D
Explanation
A $$\to$$ B $$\to$$ C (stable)
Initially no. of atoms of B = 0 at t = 0, no. of atoms of B will starts increasing & reaches maximum value when rate of decay of B = rate of formation of B.
After that maximum value, no. of atoms will starts decreasing as growth & decay both are exponential functions, so best possible graph is (d).
3
JEE Main 2021 (Online) 27th August Morning Shift
MCQ (Single Correct Answer)
There are 1010 radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? $$\left( {\sqrt 2 = 1.414} \right)$$
At time t = 0, a material is composed of two radioactive atoms A and B, where NA(0) = 2NB(0). The decay constant of both kind of radioactive atoms is $$\lambda$$. However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of NB(t) / NB(0) with respect to time t?