Modern physics Quiz 1

Question 1

In the Davisson-Germer Experiment, electrons of a certain wavelength were accelerated and made incident on a Nickel crystal to scatter. The spacing between the planes of the crystal when measured by X-ray diffraction was found to be $$0.091\,nm$$. In one particular measurement, an intensity maxima was observed when the angle between the incident beam and the detector was $$65^{\circ}$$.What was the wavelength of electrons incident on the crystal? $$(sin\,65^{\circ} = 0.91)$$

Accepted Answer

0.1656 nm

Answer

0.650 nm

Answer

0.1100 nm

Answer

0.910 nm

Question 2

Fill in the blank: Robert Millikan, much like the other physicists in 1916, was never an advocate of the particle theory of light since the wave nature of light had already been proved by the Michelson Morley experiment, and looked at Einstein’s photoelectric equation with much scrutiny. To this end, he decided to arrive at conclusive results by performing a vacuum sealed photoelectric effect experiment himself. Being an experimental physicist, his procedure was thorough and his findings ended up corroborating Einstein’s theorized photoelectric equation instead of disproving its validity since he was able to verify the value of Planck’s constant to be nearly ___ $$erg\,s$$ which was acceptable at the time. He did so by plotting a volt-frequency graph similar to the following figure. $$(	ext{Take photoelectron charge to be e =} 1.59 	imes 10^{-19}\,J)$$<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/ff141f11-422c-45d5-9fbd-1f4dc16d14fa2624833708284115462.png"/>

Accepted Answer

$$6.56 	imes 10^{-27}\,erg\,s$$

Answer

$$6.86 	imes 10^{-34}\,Js$$

Answer

$$6.62 	imes 10^{-27}\,Js$$

Answer

$$6.62 	imes 10^{-34}\,erg\,s$$

Question 3

Estimate the number of mean lives elapsed when the number of atoms in a radioactive sample reduces to 20% the original value. $$(	ext{Take}\, ln\,5 = 1.609)$$

Accepted Answer

2

Answer

3

Answer

1

Answer

4

Question 4

Whenever a string of length $$L$$ is vibrated, it emits harmonics of only definite wavelengths $$n\lambda$$. Similarly, a free particle of mass $$m$$ moving with a velocity $$v$$ is associated with its de Broglie wavelength $$\lambda$$ by virtue of its motion. What would be the kinetic energy of this free particle when it is confined to move in a straight line of length $$L$$?

Accepted Answer

$$\dfrac{n^2h^2}{8mL^2}$$

Answer

$$\dfrac{mv^2}{2m}$$

Answer

$$\dfrac{8mL^2}{n^2h^2}$$

Answer

$$\dfrac{nh}{2mL}$$

Question 5

In Rutherford’s alpha particle scattering experiment, a nucleus $$N$$ having a charge $$Ze$$ scatters an alpha particle of mass $$m$$ and charges $$2e$$ as shown in the figure. What would be the relation between its impact parameter $$b$$ and the minimum distance $$s$$ from the nucleus? What would be the minimum distance in case of a head-on collision? Take $$KE_{i}$$ as the initial kinetic energy of the alpha particle, and the nuclear electric potential as $$k\dfrac{Ze}{s}$$.<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/b396406e-3fb6-444a-9fb0-c503dd251c071671784755767094074.png"/>

Accepted Answer

$$ s^2 = k\dfrac{2Ze^2s}{KE_{i}} +b^2$$ and $$s = k\dfrac{2Ze^2}{KE_{i}}$$

Answer

$$s^2 = k\dfrac{2Ze^2s}{KE_{i}} -b^2$$ and $$s = k\dfrac{2Ze^2}{KE_{i}}$$

Answer

$$s^2 = k\dfrac{2Ze^2s}{KE_{i}}+b$$ and $$s = b$$

Answer

$$s^2 = k\dfrac{2Ze^2s}{KE_{i}}-b$$ and $$s=b^2$$