Electron guns are used in X-ray tubes. The electrons are accelerated through a relatively large voltage and directed onto a metal target, producing X-rays. (a) How many electrons per second strike the target if the current is 0.500 mA? (b) What charge strikes the target in 0.750 s?

(a) Number of electrons per second strike the target is 3.125 x 10¹⁵.

(b) Charge that strikes the target in 0.750 s is 3.75 x 10⁻⁴ C .

Explanation:

(a) Let n be the number of electrons per second strike the target. We know that current (I) is given by the relation :

I = n x e

Here e is charge of electron.

Substitute 0.500 x 10⁻³ A for I and 1.6 x 10⁻¹⁹ C for e in the above equation.

0.500 x 10⁻³ = n x 1.6 x 10⁻¹⁹

n = 3.125 x 10¹⁵

(b) Let q be the charge that strikes the target. We know that :

q = I x t

Here I is current and t is time.

Substitute 0.500 x 10⁻³ A for I and 0.750 s for t in the above equation,

q = 0.500 x 10⁻³ x 0.750

q = 3.75 x 10⁻⁴ C

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s