Question

A large cyclotron directs a beam of He++ nuclei onto a target with a beam current of 0.245 mA.

(a) How many He++ nuclei per second is this? He++ nuclei/s

(b) How long (in s) does it take for 1.35 C to strike the target? s

(c) How long (in s) before 1.20 mol of He++ nuclei strike the target? s

Please show step by step with legible writing. Thank you

Answer 1

Given that the beam current (of He ++ nuclei) is 0.245 mA .

Current is defined as the toatal amount of charge passing through a cross section in 1 second.

It means that total 0.245 mC (or 0.000245 C) charge is hitting the target in one second.

Now, He++ nuclei has two protons .

Charge on one proton = 1.602 x 10^-19 C

So, total charge on He++ ion = 2 x 1.602 x 10^-19 = 3.204 x 10^-19 C

(a) In one second 0.245 mC charge is hitting the target . And 3.204 x 10^-19 C charge is equivalent to one He++ nuclei.

So, number of He++ nuclei hitting the target per second is

He++ nuclei / s .

(b) Since in 1 second 0.245 mC charge strike the target.

So, 1.35 C of charge strike the target in  

  

(c) Since one mole of He++ nuclei consists of 6.022 x 10²³ He++ nuclei.

So, 1.20 mole of He++ nuclei = 1.20 x 6.022 x 10²³ = 7.2264 x 10²³ He++ nuclei

We know that , in one second 76.4669 x 10¹³ He++ nuclei strike the target .

So, 7.2264 x 10²³ He++ nuclei will strike the target in .

  

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