Question

A large cyclotron directs a beam of He++ nuclei onto a target with a beam current of 0.250 mA.

(a) How many He++ nuclei per second is this?
a) (3.75 X 10^16) nuclei/s
b) (1.50 X 10^16) nuclei/s
c) (6.25 X 10^16) nuclei/s
d) (2.50 X 10^16) nuclei/s

How long does it take for 1.00 C to strike the target?
a) 4,000 s
b) 2,000 s
c) 1,000 s
d) 500 s

Answer 1

The number of He++ nuclei per second is (2.50 X 10^16) nuclei/s. Thus option D is correct.

Step-by-step explanation:

In the first part of the question, to determine the number of He++ nuclei per second, we can use the formula:

Nuclei per second = Current ×
`(charge)/(charge of one nucleus)`

Given the beam current is 0.250 mA (0.250 x 10^-3 A) and the charge of He++ nuclei is twice the elementary charge (2e), we can calculate the number of nuclei per second:

Nuclei per second = 0.250 ×
`10^(-3)` A ×
`(2*1.6*10^(-19) C)/(2*1.6*10^(-19) C)` = 2.50×
`10^(16)` nuclei/s.

Thus option D is correct.

Final answer:

It takes 2,000 s for 1.00 C to strike the target. Thus option B is correct.

Step-by-step explanation:

For the second part, to find the time taken for 1.00 Coulomb of charge to strike the target, we use the formula:

Time=
`(Charge)/(Current)`

Given 1.00C of charge and the beam current of 0.250 mA, we calculate:

Time=
`(1.00C)/(0.250*10^(-3) A)`= 2,000 s

Therefore, the answer to the second part of the question is 2,000 seconds for 1.00 Coulomb of charge to strike the target. Thus option B is correct.