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20 November, 15:15

Each metal is illuminated with 400 nm (3.10 eV) light. Rank the metals on the basis of the maximum kinetic energy of the emitted electrons. (If no electrons are emitted from a metal, the maximum kinetic energy is zero, so rank that metal as smallest.) Rank from largest to smallest. To rank items as equivalent, overlap them.

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  1. 20 November, 16:37
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    K. E (K) > K. E (Cs) > 0 (others)

    Explanation:

    Given the Work functions of the metal as

    Aluminium (Wo) = 4eV

    Platinum (Wo) = 6.4eV

    Cesium (Wo) = 2.1eV

    Beryllium (Wo) = 5.0eV

    Magnesium (Wo) = 3.7eV

    Potassium (Wo) = 2.3eV

    Using the formula:

    K. E = hf - Wo ... (1)

    Wo = hfo ... (2)

    From these the fo can be calculated for all the metals

    Where K. E = Kinetic Energy

    hf = energy of illumination = 3.10eV

    h is Planck constant and has the value 6.6 * 10^-34JS^-1

    The frequency f of the illumination is given by

    f = 3.10 * 1.6 * 10^-19/6.6 * 10^-34

    f = 7.51 * 10¹⁴ Hz ... (*)

    Now an electron is only ejected if the threshold frequency of the metal is reached.

    The work function has a threshold frequency (fo) for all the metals and this minimum frequency required to required to remove an electron from the surface of a metal.

    We need to compare f with fo

    If fo > = f there is emission, otherwise there is no emission

    So using (2) we calculate for all fo and compare with f

    K. E (Al) = 3.10 - 4.0 - 3.10 = - 0.9eV, fo = 9.70 * 10¹⁴ Hz (no emission)

    K. E (Pt) = 3.10 - 6.40 = - 3.30eV, fo = 1.55 * 10^15 Hz, (no emission)

    K. E (Cs) = 3.10 - 2.10 = - 1.0eV, fo = 5.09*10¹⁴ Hz, (emission)

    K. E (Be) = 3.10-5.0 = - 1.90eV, fo = 12.12 * 10^15 Hz., (no emission)

    K. E (Mg) = 3.10-3.70 = - 0.6eV, fo = 8.97 * 10¹⁴Hz, (no emission)

    K. E (K) = 3.10 - 2.30 = 0.9eV, fo = 5.58 * 10¹⁴ Hz, (emission)

    So the metals whose electron gain Kinetic energy are:

    Cesium

    Potassium

    Others have zero kinetic energy since no electron is emitted.

    Hence the rank is:

    K. E (K) > K. E (Cs) > 0 (others)
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