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When a certain metal was irradiated with light of frequency 1.6 x 1016 Hz, the photoelectrons emitted had twice the kinetic energy as did photoelectrons emitted when the same metal was irradiated with light of frequency 1.0 x 1016 Hz. Thus, threshold frequency for the metal is
  • a)
    1.0 x1015 Hz
  • b)
    2.0 x105 Hz
  • c)
    4.0 x 1015Hz
  • d)
    6.0 x 1015 Hz
Correct answer is option 'C'. Can you explain this answer?
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When a certain metal was irradiated with light of frequency 1.6 x 1016...
For photoelectric effect

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When a certain metal was irradiated with light of frequency 1.6 x 1016...
Explanation:
The kinetic energy of the emitted photoelectrons is directly proportional to the frequency of the incident light. The threshold frequency is the minimum frequency of light required to emit photoelectrons from a metal surface.

Given:
Frequency of light for higher kinetic energy photoelectrons = 1.6 x 10^16 Hz
Frequency of light for lower kinetic energy photoelectrons = 1.0 x 10^16 Hz

Calculations:
Let the threshold frequency be denoted by f. According to the given information, the kinetic energy of the photoelectrons is directly proportional to the frequency of the incident light:
1.6 x 10^16 Hz = 2 * (1.0 x 10^16 Hz - f)
Solving for f:
1.6 x 10^16 Hz = 2.0 x 10^16 Hz - 2f
2.0 x 10^16 Hz - 1.6 x 10^16 Hz = 2f
0.4 x 10^16 Hz = 2f
f = 0.4 x 10^16 Hz / 2
f = 0.2 x 10^16 Hz
f = 2.0 x 10^15 Hz
Therefore, the threshold frequency for the metal is 2.0 x 10^15 Hz, which corresponds to option (c).
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When a certain metal was irradiated with light of frequency 1.6 x 1016 Hz, the photoelectrons emitted had twice the kinetic energy as did photoelectrons emitted when the same metal was irradiated with light of frequency 1.0 x 1016 Hz. Thus, threshold frequency for the metal isa)1.0 x1015 Hzb)2.0 x105Hzc)4.0 x 1015Hzd)6.0 x 1015HzCorrect answer is option 'C'. Can you explain this answer?
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