When UV light of wavelength 295nm falls on a metal surface, the maximum kinetic energy of emitted electrons is 1.50eV.
What is the work function of the metal?
W0 in eV
To find the work function (W0) of the metal, we can use the equation:
Energy of a photon (E) = Work function (W0) + Kinetic energy of emitted electron (K.E.)
The energy of a photon can be calculated using the equation:
Energy of a photon (E) = Planck's constant (h) * Speed of light (c) / Wavelength (λ)
Given:
Wavelength (λ) = 295 nm = 295 x 10^-9 m
Kinetic energy of emitted electron (K.E.) = 1.50 eV
First, let's convert the wavelength from nanometers (nm) to meters (m):
λ = 295 x 10^-9 m
Now, let's calculate the energy of a photon:
E = (6.626 x 10^-34 J.s) * (3.00 x 10^8 m/s) / (295 x 10^-9 m)
E ≈ 6.70 x 10^-19 J
Since 1 eV is equal to approximately 1.602 x 10^-19 J, let's convert the kinetic energy of emitted electron (K.E.) from eV to Joules (J):
K.E. = 1.50 eV * (1.602 x 10^-19 J/eV)
K.E. ≈ 2.40 x 10^-19 J
Now we can substitute the values into the equation:
2.40 x 10^-19 J = W0 + 6.70 x 10^-19 J
To isolate W0, let's rearrange the equation:
W0 = 2.40 x 10^-19 J - 6.70 x 10^-19 J
W0 ≈ -4.30 x 10^-19 J
The work function (W0) of the metal is approximately -4.30 x 10^-19 J.
To find the work function (W0) of the metal, you can use the equation:
Kinetic energy (KE) of the emitted electrons = Energy of incident photons - Work function (W0)
In this case, the kinetic energy (KE) of the emitted electrons is given as 1.50 eV. The energy of incident photons can be calculated using the equation:
Energy of incident photons = Planck's constant (h) * Speed of light (c) / Wavelength
Here, the wavelength (λ) is given as 295 nm, which is equivalent to 295 × 10^-9 meters.
So, the energy of incident photons can be calculated as:
Energy of incident photons = (6.626 × 10^-34 J·s) * (3 × 10^8 m/s) / (295 × 10^-9 m)
Now, let's convert this energy into electron volts (eV):
1 eV = 1.602 × 10^-19 J
So, the energy of incident photons in eV is:
Energy of incident photons = (6.626 × 10^-34 J·s) * (3 × 10^8 m/s) / (295 × 10^-9 m) / (1.602 × 10^-19 J/eV)
Once you have the energy of incident photons in eV, you can plug it into the first equation to find the work function:
1.50 eV = Energy of incident photons - W0
Now you can rearrange the equation to find W0:
W0 = Energy of incident photons - 1.50 eV
By substituting the value of the energy of incident photons into the equation and performing the calculation, you can find the work function (W0) in eV.