What is the longest wavelength of light that will emit electrons from a metal whose work function is 3.10eV?
Well, prepare yourself for a bit of a physics joke. The longest wavelength of light that will emit electrons from a metal with a work function of 3.10eV is actually so long that it's practically invisible. It's like trying to find a needle in a haystack using a microscope. So, in other words, you won't be able to see it, but trust me, it's there!
To determine the longest wavelength of light that will emit electrons from a metal, we can use the equation:
λ = hc/E
where:
λ is the wavelength of light,
h is Planck's constant (6.626 × 10^-34 J·s),
c is the speed of light (3.00 × 10^8 m/s), and
E is the energy of a photon.
Since the work function is given in electron volts (eV), we need to convert it to joules (J) before we can proceed.
1 eV = 1.602 × 10^-19 J
So, the work function in joules can be calculated as follows:
work function (J) = work function (eV) × (1.602 × 10^-19 J/eV)
= 3.10 eV × (1.602 × 10^-19 J/eV)
= 4.9652 × 10^-19 J
Now, we can plug the values into the equation mentioned earlier:
λ = (6.626 × 10^-34 J·s * 3.00 × 10^8 m/s) / (4.9652 × 10^-19 J)
Calculating this will give us the longest wavelength of light that will emit electrons from the metal.
To determine the longest wavelength of light that will emit electrons from a metal, we need to use the equation:
λ = c / f
where λ is the wavelength, c is the speed of light (approximately 3.00 x 10^8 meters per second), and f is the frequency of the light.
The energy of the incident light, E, can be represented using the equation:
E = hf
where h is Planck's constant (approximately 6.63 x 10^-34 joule-seconds) and f is the frequency.
The work function, W, is the minimum energy required to remove an electron from the metal's surface. It can be represented in terms of energy as:
W = h * f0
where f0 is the threshold frequency, the minimum frequency required to emit electrons.
Since we are dealing with light, which is electromagnetic radiation, we can relate frequency to wavelength using the equation:
c = λ * f
To solve for the threshold frequency f0, we can rearrange the equation as follows:
f0 = c / λ
Since the threshold frequency represents the minimum frequency required to emit electrons, we can calculate the threshold energy, E0, by substituting f0 into the energy equation:
E0 = h * f0 = h * (c / λ)
Given that the work function W is 3.10 eV, we can convert this value to joules by multiplying it by the conversion factor 1.60 x 10^-19 J/eV:
W = 3.10 eV * (1.60 x 10^-19 J/eV)
Now, we can solve for the threshold frequency f0 using the expression:
W = h * f0
Substituting the values for W and h:
3.10 eV * (1.60 x 10^-19 J/eV) = (6.63 x 10^-34 J·s) * f0
Solving for f0:
f0 = (3.10 eV * 1.60 x 10^-19 J/eV) / (6.63 x 10^-34 J·s)
Once we have the value for f0, we can determine the longest wavelength λmax using the equation:
λ = c / f0
Substituting the values for c and f0:
λmax = (3.00 x 10^8 m/s) / f0
Calculating λmax will give us the answer to your question.
The wavelength L that satisfies the equation
h c/L = 3.10 eV* (1.6*10^-19 J/eV)
h is Planck's constant. c is the speed of light, of course.
hc/L is the photon energy