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Structure of Atom question

2020 · 2 Sep · Shift 2 · Q3
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Structure of Atom question

2020 · 2 Sep · Shift 2 · Q3

JEE MainChemistryStructure of AtomNumerical+4 / −1
The work function of sodium metal is 4.41 ×\times× 10–19 J. If photons of wavelength 300 nm are incident on the metal, the kinetic energy of the ejected electrons will be (h = 6.63 ×\times× 10–34 J s; c = 3 ×\times× 108 m/s) ‾\underline{\hspace{2cm}}​ × 10–21 J.
Numerical answer
View written solutionFree

Correct answer: 222

  1. Use Einstein’s photoelectric equation

    K.E.=hν−ϕ=hcλ−ϕK.E. = h\nu - \phi = \frac{hc}{\lambda} - \phiK.E.=hν−ϕ=λhc​−ϕ

    where:

    • ϕ=4.41×10−19 J\phi = 4.41 \times 10^{-19}\,\text{J}ϕ=4.41×10−19J
    • h=6.63×10−34 J sh = 6.63 \times 10^{-34}\,\text{J s}h=6.63×10−34J s
    • c=3×108 m/sc = 3 \times 10^8\,\text{m/s}c=3×108m/s
    • λ=300 nm=300×10−9 m\lambda = 300\,\text{nm} = 300 \times 10^{-9}\,\text{m}λ=300nm=300×10−9m

  2. Calculate energy of incident photon

    E=hcλE = \frac{hc}{\lambda}E=λhc​

    E=(6.63×10−34)(3×108)300×10−9E = \frac{(6.63 \times 10^{-34})(3 \times 10^8)}{300 \times 10^{-9}}E=300×10−9(6.63×10−34)(3×108)​

    First, numerator:

    6.63×10−34×3×108=19.89×10−266.63 \times 10^{-34} \times 3 \times 10^8 = 19.89 \times 10^{-26}6.63×10−34×3×108=19.89×10−26

    Denominator:

    300×10−9=3×10−7300 \times 10^{-9} = 3 \times 10^{-7}300×10−9=3×10−7

    So,

    E=19.89×10−263×10−7=6.63×10−19 JE = \frac{19.89 \times 10^{-26}}{3 \times 10^{-7}} = 6.63 \times 10^{-19}\,\text{J}E=3×10−719.89×10−26​=6.63×10−19J

  3. Calculate kinetic energy of ejected electron

    K.E.=6.63×10−19−4.41×10−19K.E. = 6.63 \times 10^{-19} - 4.41 \times 10^{-19}K.E.=6.63×10−19−4.41×10−19

    K.E.=2.22×10−19 JK.E. = 2.22 \times 10^{-19}\,\text{J}K.E.=2.22×10−19J

  4. Express in the required form

    We need:

    ‾×10−21 J\underline{\hspace{2cm}} \times 10^{-21}\,\text{J}​×10−21J

    Since,

    2.22×10−19=222×10−212.22 \times 10^{-19} = 222 \times 10^{-21}2.22×10−19=222×10−21

  5. Final answer

    222\boxed{222}222​

  6. Comparison with stored correct answer

    Stored correct answer = 222222222

    This matches the derived answer.

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