Question 5 of 62beginner🔧 ApplyNumerical2 marks

Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wavenumber (ν̄) of the yellow light.

Correct Answer

(frequency) 5.172×1014 s−15.172 \times 10^{14} \text{ s}^{-1}

(wavenumber) 1.724×106 m−11.724 \times 10^6 \text{ m}^{-1} or 1.724×104 cm−11.724 \times 10^4 \text{ cm}^{-1}

Exercise: EXERCISES | Q: 2.5 | (Page 41)
For More Understanding

Explanation

To find the frequency and wavenumber of the yellow light, we first convert the given wavelength from nanometers to meters. The wavenumber is the reciprocal of the wavelength, and the frequency is calculated using the formula ν=cλ\nu = \frac{c}{\lambda}, where cc is the speed of light (3×108 m s−13 \times 10^8 \text{ m s}^{-1}).

Solution Steps

  1. Step 1: Convert wavelength to meters

    λ=580 nm=580×10−9 m=5800×10−10 m\lambda = 580 \text{ nm} = 580 \times 10^{-9} \text{ m} = 5800 \times 10^{-10} \text{ m}

  2. Step 2: Calculate wavenumber (νˉ\bar{\nu})

    νˉ=1λ=15800×10−10 m=1.724×106 m−1=1.724×104 cm−1\bar{\nu} = \frac{1}{\lambda} = \frac{1}{5800 \times 10^{-10} \text{ m}} = 1.724 \times 10^6 \text{ m}^{-1} = 1.724 \times 10^4 \text{ cm}^{-1}

  3. Step 3: Calculate frequency (ν\nu)

    ν=cλ=3×108 m s−15800×10−10 m=5.172×1014 s−1\nu = \frac{c}{\lambda} = \frac{3 \times 10^8 \text{ m s}^{-1}}{5800 \times 10^{-10} \text{ m}} = 5.172 \times 10^{14} \text{ s}^{-1}
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