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? (b) How long does it take for 1.00 C to strike the target? (c) How long before 1.00 mol of He++ nuclei strike the target?

Answer 1

Answer:

a. 7.8*10¹⁴ He⁺⁺ nuclei/s

b. 4000s

c. 7.7*10⁸s

Explanation:

I = 0.250mA = 2.5 * 10⁻³A

Q = 1.0C

1 e- contains 1.60 * 10⁻¹⁹C

But He⁺⁺ Carrie's 2 charge = 2 * 1.60*10⁻¹⁹C = 3.20*10⁻¹⁹C

(A).

No. Of charge per second = current passing through / charge

1 He⁺⁺ = 2.50 * 10⁻⁴ / 3.2*10⁻¹⁹C

1 He⁺⁺ = 7.8 * 10¹⁴ He⁺⁺ nuclei

(B).

I = Q / t

From this equation, we can determine the time it takes to transfer 1.0C

I = 1.0 / 2.5*10⁻⁴ = 4000s

(C).

Time it takes for 1 mol of He⁺⁺ to strike the target =?

Using Avogadro's ratio,

1.0 mole of He = (6.02 * 10²³ ions/mol ) * (1 / 7.81*10¹⁴ He ions)

Note : ions cancel out leaving the value of the answer in mols.

1.0 mol of He = 7.7 * 10⁸s