Question 8 of 62intermediate🔧 ApplyNumerical2 marks

What is the number of photons of light with a wavelength of 4000 pm that provide 1J of energy?

Correct Answer

2.012×10162.012 \times 10^{16} photons

Exercise: EXERCISES | Q: 2.8 | (Page 41)
For More Understanding

Explanation

To find the number of photons, we first calculate the energy of a single photon using the formula E=hc/λE = hc/\lambda. The given wavelength is 4000 pm, which must be converted to meters. Then, we divide the total energy (1 J) by the energy of a single photon to get the total number of photons required.

Solution Steps

  1. Step 1: Convert the given wavelength into meters.

    λ=4000 pm=4000×10−12 m=4×10−9 m\lambda = 4000 \text{ pm} = 4000 \times 10^{-12} \text{ m} = 4 \times 10^{-9} \text{ m}

  2. Step 2: Calculate the energy of one photon using the expression E=hcλE = \frac{hc}{\lambda}.

    h=6.626×10−34 J sh = 6.626 \times 10^{-34} \text{ J s} c=3×108 m s−1c = 3 \times 10^{8} \text{ m s}^{-1} E=6.626×10−34 J s×3×108 m s−14×10−9 m=4.969×10−17 JE = \frac{6.626 \times 10^{-34} \text{ J s} \times 3 \times 10^{8} \text{ m s}^{-1}}{4 \times 10^{-9} \text{ m}} = 4.969 \times 10^{-17} \text{ J}

  3. Step 3: Calculate the number of photons that provide 1 J of energy. Number of photons = Total EnergyEnergy of one photon\frac{\text{Total Energy}}{\text{Energy of one photon}} Number of photons = 1 J4.969×10−17 J=2.012×1016\frac{1 \text{ J}}{4.969 \times 10^{-17} \text{ J}} = 2.012 \times 10^{16}

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