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For the wavelength associated with a frequency of 50 kHz. Although the question mentions an "electron produced from the surface of a metal," the given frequency is characteristic of an ele

Physics

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The question asks for the wavelength associated with a frequency of 50 kHz50 \, \text{kHz}. Although the question mentions an "electron produced from the surface of a metal," the given frequency is characteristic of an electromagnetic wave. We will calculate the wavelength of an electromagnetic wave with this frequency.

  1. Convert the given frequency from kilohertz (kHz) to hertz (Hz).

    The frequency f=50 kHzf = 50 \, \text{kHz}.
    Since 1 kHz=103 Hz1 \, \text{kHz} = 10^3 \, \text{Hz},

    f=50×103 Hzf = 50 \times 10^3 \, \text{Hz}
  2. Use the formula relating the speed of light (cc), wavelength (λ\lambda), and frequency (ff).

    The speed of light in a vacuum is approximately c=3.00×108 m/sc = 3.00 \times 10^8 \, \text{m/s}.
    The formula is:

    c=λfc = \lambda f

    To find the wavelength, rearrange the formula:

    λ=cf\lambda = \frac{c}{f}
  3. Substitute the values and calculate the wavelength.

    λ=3.00×108 m/s50×103 Hz\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{50 \times 10^3 \, \text{Hz}} λ=3.00×1085.0×104 m\lambda = \frac{3.00 \times 10^8}{5.0 \times 10^4} \, \text{m} λ=(3.005.0)×108−4 m\lambda = \left(\frac{3.00}{5.0}\right) \times 10^{8-4} \, \text{m} λ=0.6×104 m\lambda = 0.6 \times 10^4 \, \text{m} λ=6×103 m\lambda = 6 \times 10^3 \, \text{m}
  4. Compare the calculated wavelength with the given options.

    (A) 6×10−6 m6 \times 10^{-6} \, \text{m}
    (B) 6×103 m6 \times 10^3 \, \text{m}
    (C) 5×10−6 m5 \times 10^{-6} \, \text{m}
    (D) 5×103 m5 \times 10^3 \, \text{m}

    The calculated wavelength matches option (B).

    The final answer is B) 6×103 m\boxed{\text{B) } 6 \times 10^3 \, \text{m}}.

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