A proton and an α-particle have the same de-Broglie wavelength. Determine the ratio of (i) their accelerating potentials (ii) their speeds.
Show that the radius of the orbit in hydrogen atom varies as , where n is the principal quantum number of the atom.
Use the mirror equation to show that an object placed between f and 2f of a concave mirror produces a real image beyond 2f?
Mirror formula is given by,
where,
u is the distance of the object from the mirror,
v is the distance of the image from the mirror, and
f is the focal length of the mirror.
For a concave mirror, f < 0.
Object distance is negative for an object on the left side. i.e., u< 0.
Given, f < u <2f.
Subtracting throughout from , we get
Therefore, the image formed is negative and is on the left side.
Also, the inequality implies, 2f > v. i.e., |2f| < |v|.
That is, the real image is formed beyond 2f.
(i) A giant refracting telescope has an objective lens of focal length 15 m. If an eye piece of focal length 1.0 cm is used, what is the angular magnification of the telescope?
(ii) If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens ? The diameter of the moon is 3.48 × 106 m and the radius of lunar orbit is 3.8 × 108 m.Write Einstein’s photoelectric equation and mention which important features in photoelectric effect can be explained with the help of this equation. The maximum kinetic energy of the photoelectrons gets doubled when the wavelength of light incident on the surface changes from to
. Derive the expressions for the threshold wavelength
and work function for the metal surface.
In the study of Geiger-Marsdon experiment on scattering of α particles by a thin foil of gold, draw the trajectory of -particles in the coulomb field of target nucleus. Explain briefly how one gets the information on the size of the nucleus from this study. From the relation R = Ro A1/3 where Ro is constant and A is the mass number of the nucleus, show that nuclear matter density is independent of A.
Distinguish between nuclear fission and fusion. Show how in both these processes energy is released.
Calculate the energy release in MeV in the deuterium-tritium fusion reaction: