Question 7 of 62intermediate🔧 ApplyNumerical2 marks

Calculate the wavelength, frequency and wavenumber of a light wave whose period is 2.0×102.0 \times 10⁻¹⁰ s.

Correct Answer

Wavelength = 6.0×10−26.0 \times 10^{-2} m, Frequency = 5.0×1095.0 \times 10^9 Hz, Wavenumber = 16.6716.67 m−1^{-1}

Exercise: EXERCISES | Q: 2.7 | (Page 41)
For More Understanding

Explanation

To find the required values, we first calculate the frequency using the given period. Then, using the speed of light (c=3.00×108c = 3.00 \times 10^8 m s−1^{-1}), we calculate the wavelength. Finally, the wavenumber is found by taking the reciprocal of the wavelength.

Solution Steps

  1. Step 1: Calculate Frequency Given period, T=2.0×10−10T = 2.0 \times 10^{-10} s. Frequency (vv) is the reciprocal of the period: v=1T=12.0×10−10 s=5.0×109 s−1v = \frac{1}{T} = \frac{1}{2.0 \times 10^{-10} \text{ s}} = 5.0 \times 10^9 \text{ s}^{-1} (Hz)

  2. Step 2: Calculate Wavelength Using the relation λ=cv\lambda = \frac{c}{v}, where c=3.00×108 m s−1c = 3.00 \times 10^8 \text{ m s}^{-1}:

    λ=3.00×108 m s−15.0×109 s−1=0.06 m=6.0×10−2 m\lambda = \frac{3.00 \times 10^8 \text{ m s}^{-1}}{5.0 \times 10^9 \text{ s}^{-1}} = 0.06 \text{ m} = 6.0 \times 10^{-2} \text{ m}

  3. Step 3: Calculate Wavenumber Wavenumber (νˉ\bar{\nu}) is the reciprocal of wavelength:

    νˉ=1λ=16.0×10−2 m=16.67 m−1\bar{\nu} = \frac{1}{\lambda} = \frac{1}{6.0 \times 10^{-2} \text{ m}} = 16.67 \text{ m}^{-1}
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