A metal with a work function of 2.40 eV is illuminated by a beam of monochromatic light. If the stopping potential is 2.5V, what is the wavelength of the light?
energy is .1ev
energy= plancks constant*c/lambda
change energy from ev to joules, then solve for lambda
To find the wavelength of the light, we can use the equation:
eV = hν - Φ
where:
- e is the elementary charge (1.6 x 10^-19 C)
- V is the stopping potential (2.5 V)
- h is Planck's constant (6.63 x 10^-34 J·s)
- ν is the frequency of the light
- Φ is the work function of the metal (2.40 eV)
First, we need to convert the work function from eV to joules:
Φ = 2.40 eV * (1.6 x 10^-19 J/eV) = 3.84 x 10^-19 J
Next, we rearrange the equation to solve for the frequency (ν):
hν = eV + Φ
ν = (eV + Φ) / h
Now, we can calculate the frequency:
ν = (1.6 x 10^-19 C * 2.5 V + 3.84 x 10^-19 J) / (6.63 x 10^-34 J·s)
Finally, we can use the speed of light equation (c = λν), where c is the speed of light (3 x 10^8 m/s), to solve for the wavelength (λ):
λ = c / ν
By substituting the values and calculating, we can find the wavelength of the light.