A metal whose threshold frequency is 1.80×1015 s-1 emits an electron with a velocity of 7.24×105 m/s when radiation of 2.13×1015 s-1 strikes the metal.Use these data to calculate the mass of the electron.
To calculate the mass of the electron, we need to apply the concept of the photoelectric effect and use the given data.
The photoelectric effect states that when light of a certain frequency strikes a metal surface, electrons can be emitted if the frequency of the light surpasses a minimum threshold value. This threshold value is dependent on the metal.
The energy of a single photon can be calculated using the equation:
E = hf,
where E is the energy of the photon, h is Planck's constant (6.626 × 10^-34 J·s), and f is the frequency of the photon.
The kinetic energy of the emitted electron can be calculated using the equation:
KE = (1/2)mv^2,
where KE is the kinetic energy, m is the mass of the electron, and v is the velocity of the electron.
Considering the conservation of energy, the energy of the photon that is absorbed by the electron (E) is equal to its kinetic energy (KE). Therefore, we can equate these two equations:
hf = (1/2)mv^2.
Rearranging the equation to solve for mass (m), we have:
m = (2hf) / v^2.
Now let's substitute the given values into the equation:
h = 6.626 × 10^-34 J·s,
f = 2.13 × 10^15 s^-1,
v = 7.24 × 10^5 m/s.
Plugging in these values, we get:
m = (2 * (6.626 × 10^-34 J·s) * (2.13 × 10^15 s^-1)) / (7.24 × 10^5 m/s)^2.
Simplifying this expression, we find:
m ≈ 9.11 × 10^-31 kg.
Therefore, the mass of the electron, based on the given data, is approximately 9.11 × 10^-31 kg.