Respuesta :
Answer:
Minimun energy to eject an electron: 2.03 × 10⁻¹⁹ J.
The maximum kinetic energy is 6.46 × 10⁻¹⁹ J.
Explanation:
Find the minimum energy needed to eject electrons from a metal with a threshold frequency of 3.07 × 10¹⁴ s⁻¹
The minimum energy to eject an electron from a metal can be calculated using the Planck-Einstein equation.
E = h . ν
where,
h is the Planck's constant (6.63 × 10⁻³⁴ J . s)
ν is the threshold frequency
In this case,
E = 6.63 × 10⁻³⁴ J . s × 3.07 × 10¹⁴ s⁻¹ = 2.03 × 10⁻¹⁹ J
With what maximum kinetic energy will electrons be ejected when this metal is exposed to light with a wavelength of 235 nm?
We can find the energy provided by the light using the Planck-Einstein equation. First, we need its frequency, which can be calculated from the following expression:
c = λ × ν
where,
c is the speed of light (3.00 × 10⁸ m/s)
λ is the wavelength
Then,
[tex]\nu = \frac{c}{\lambda } =\frac{3.00 \times 10^{8}m/s }{235 \times 10^{-9} m } =1.28 \times 10^{15} s^{-1}[/tex]
Let's call total energy T.
T = h . ν = 6.63 × 10⁻³⁴ J . s × 1.28 × 10¹⁵ s⁻¹ = 8.49 × 10⁻¹⁹ J
From the total energy provided by the light (T), a part is used to eject the electron (E) and another part goes to the kinetic energy of the electron (K).
T = E + K
K = T - E = 8.49 × 10⁻¹⁹ J - 2.03 × 10⁻¹⁹ J =6.46 × 10⁻¹⁹ J
A) The minimum energy required to eject electrons from the metal that has the threshold frequency of 3.07 × 10¹⁴ /s is; E = 2.034 × 10⁻¹⁹ J
B) The maximum kinetic energy when the metal is exposed to a light with wavelength of 235 nm is; E_k = 6.427 × 10⁻¹⁹ J
A) We are given;
Threshold frequency; ν = 3.07 × 10¹⁴ /s
Formula for the minimum energy required to eject electrons from the metal that has the threshold frequency above is;
E = hν
Where;
h is Planck's constant = 6.626 × 10⁻³⁴ J.s
ν is threshold frequency
Thus;
E = 3.07 × 10¹⁴ × 6.626 × 10⁻³⁴
E = 2.034 × 10⁻¹⁹ J
B) We want to find the max kinetic energy when the metal is exposed to a light with wavelength of; λ = 235 nm = 235 × 10⁻⁹ m
Let's first find the threshold frequency of this light wave from the formula;
ν = c/λ
Where:
c is speed of light = 3 × 10⁸ m/s
Thus;
ν = (3 × 10⁸)/(235 × 10⁻⁹)
ν = 1.277 × 10¹⁵
Thus, Light energy is;
E_light = 1.277 × 10¹⁵ × 6.626 × 10⁻³⁴
E_Light = 8.461 × 10⁻¹⁹ J
Now this total light energy will be split as part of it will be used to eject the electron while the remaining will serve as kinetic energy. Thus;
E_k + E = E_light
E_k = E_light - E
E_k = (8.461 × 10⁻¹⁹) - (2.034 × 10⁻¹⁹)
E_k = 6.427 × 10⁻¹⁹ J
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