Respuesta :
(a) The highest possible rate of kinetic energy is -2.2 eV and the highest possible rate of speed is 2.3 × 10⁶ m/s.
(b) The length of the radiation's wave is 86 nm.
(c) The lowest frequency of visible light is 3.5 x 10¹⁴ Hz.
SOLUTION
To solve this problem, we can use the following equations:
- The maximum kinetic energy of the electrons emitted from the sodium surface is given by:
KEmax = Work function - Potential difference
- The maximum speed of the electrons is given by:
vmax = sqrt (2 × KEmax ÷ m)
where m is the mass of the electron.
- The incident radiation wavelength can be calculated using the Planck-Einstein equation:
E = h × f
where E is the energy of the incident radiation, h is the Planck constant, and f is the frequency of the radiation.
- The minimum frequency required for photoemission can be calculated using the work function of the sodium surface:
fmin = Work function ÷ h
- Using these equations, we can calculate the following:
(a) The maximum kinetic energy of the electrons is given by:
KEmax = 2.3 eV - 4.5 V = -2.2 eV
Hence, the maximum kinetic energy is -2.2 eV.
- The maximum speed of the electrons is given by:
vmax = sqrt(2 × (-2.2 eV) ÷ (9.1 × 10⁻³¹ kg)) = 2.3 × 10⁶ m/s
Hence the maximum speed is 2.3 × 10⁶ m/s.
(b) The incident radiation wavelength can be calculated using the Planck-Einstein equation:
E = h × f
f = E ÷ h
f = 2.3 eV / (6.6 × 10⁻³⁴ J × s) = 3.5 × 10¹⁴ Hz
lambda = c ÷ f
lambda = (3.0 x 10⁸ m/s) ÷ (3.5 x 10¹⁴ Hz) = 8.6 x 10⁻⁷ m = 86 nm.
Hence, the wavelength of the radiation is 86 nm.
(c) The minimum frequency required for photoemission can be calculated using the work function of the sodium surface:
fmin = 2.3 eV ÷ (6.6 × 10⁻³⁴ J × s) = 3.5 × 10¹⁴ Hz
Hence, the minimum frequency of light is 3.5 × 10¹⁴ Hz.
Learn more about kinetic energy here:
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