2000 - JAMB Physics Past Questions and Answers - page 3

V = 72m

U = Magnification = 24

But Magnification = V/U

∴ 24 = 72/U

U = 72/24

U = 3.0m

When a charged particle is accelerated across a region of p.d. V Volt, the work done is the product of the charge Q and the p.d. V

i.e. Work done = Q x V

But this work done is equal to the K.E. imparted to the charge given by K.E = 1/2MV², where V is the velocity of the charge = Q x V = 1/2MV²

∴ p.d V = (1/2MV²)/Q

= 1/2 x 9.1^-31 x [4 x 10⁷]²/1.6 x 10^-19

= 8 x 9.1 x 10²/1.6

= 4550V

= 4.55 x 10³V

In thermonuclear reactions,

Energy = ∆mC²

∆m = Change in Mass

C = Speed of light

∴ 5.02 x 10^-27 - 5.01 x 10^-27 x [3 x 10⁸]²

0.01 x 10^-27 x 9 x 10¹⁶

E = 9.0 x 10^-13J

In general, gases conduct electricity under reduced pressure and high voltage/potential.

But from Ohms Law, current is directly proportional to voltage. Thus high current presupposes high voltage.

Power input = 3KW = 3000W

Voltage = 1.5KV = 1500V

Current (I) = P/V = 3000/1500 = 2Amps.

∴ Power loss in the cables = I²R

= 2 x 2 x 20

= 80W

Energy imparted by the accelerating system = e x V, where V is the accelerating potential; and this energy is equal to the energy of the X-ray, give by hf

e x V = hf

∴ V = hf/e

(6.63 x 10^-34 x 1.6 x 10^-16)/1.6 x 10^-19

= 6.63 x 10 = 66.3V

1/64 is the usual fraction left of any radio active material after 4 half-lives, since 1/64 = (1/2)⁶

This implies that 6 half lives have elapsed.

Thus 6 half lives = 120 years

∴ 1 half life = 120/6 = 20 years