Short Answer Type
Long Answer TypeDerive the formula for angular magnification of a compound microscope, when the final image is formed at least distance of distinct vision. Draw the required ray diagram.
Give the expression for the velocity of electron in the first orbit of Hydrogen atom and for the radius in the ground state of Hydrogen atom.
Hence derive the expression for the kinetic energy of the electron.
Suppose e, m and v be the charge, mass and velocity of the electron measured in coulomb, kg and metre/sec respectively and r is the radius circle.
Now, the positive charge on the nucleus is Ze, where Z is the atomic number (in case of hydrogen atom Z = 1). As the centripetal force Fis by the electrostatic force of attraction,
(See Fig.), we have
From eqn. (i) and (ii), we get
From the first postulate,
Angular momentum of the electron is given b,
Dividing (i) by (ii), we get
This expression for the kinetic energy of the electron in Bohr model of hydrogen atom.
In Millikan’s oil drop experiment, a charged oil drop of density 880 kg/m3 is held stationary between two parallel plates 6.0 mm apart at a potential difference of 1000 volts. When electric field E is switched off, the oil drop was observed to fall a distance of 2.0 mm in 35.7 seconds. [4]
(i) Find the radius of oil drop.
Given :
η for air = 1.8 x 10-5 poise
Density of air = 1.29 kg/m3
Use g = 9.81 m/s2
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