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10 July, 11:08

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?

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  1. 10 July, 12:55
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    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
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