Find velocity of electron emitted by metal whose threshold frequency is 2.1*10^14 and when exposed to visible light wavelength of 5.09*10^-7

5.09E-7WHAT.

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To find the velocity of an electron emitted by a metal, you can use the concept of the photoelectric effect. The equation that relates the energy of a photon to the threshold frequency, the frequency of the incident light, and the work function of the metal is:

E = hf = ϕ + (1/2)mv^2

Where:
E is the energy of the photon,
h is Planck's constant (6.626 × 10^-34 J·s),
f is the frequency of the incident light,
ϕ is the work function (the minimum amount of energy required to remove an electron from the metal surface), and
m and v are the mass and velocity of the electron, respectively.

Given that the threshold frequency (f) of the metal is 2.1 × 10^14 Hz and the wavelength (λ) of the visible light is 5.09 × 10^-7 m, you can determine the frequency using the equation:

c = λf

Where:
c is the speed of light (approximately 3 × 10^8 m/s).

Rearrange the equation to solve for f:

f = c / λ

Substitute the given values into the equation to find the frequency (f) of the incident light:

f = (3 × 10^8 m/s) / (5.09 × 10^-7 m)

Calculate f:

f ≈ 5.89 × 10^14 Hz

Now that you have the frequency of the incident light, you can calculate the energy of the photon using the formula:

E = hf

Substitute the values into the equation:

E = (6.626 × 10^-34 J·s) × (5.89 × 10^14 Hz)

Calculate E:

E ≈ 3.9 × 10^-19 J

Since the emitted electron has energy E, which is equal to the sum of its kinetic energy (1/2)mv^2 and the work function (ϕ), you can rearrange the equation to solve for v:

(1/2)mv^2 = E - ϕ

Rearrange the equation:

v^2 = (2(E - ϕ)) / m

Substitute the known values and solve for v:

v^2 = (2 × (3.9 × 10^-19 J - ϕ)) / m

Now, without knowing the specific metal and its work function, it's not possible to provide an accurate value for v. The work function varies for different metals. However, you can use this equation to calculate the velocity by substituting the appropriate work function (ϕ) for the specific metal you are interested in.

Note: If you are given the work function or specific metal, you can directly substitute its value into the equation to calculate the velocity.