It takes 254 kJ/mol to eject electrons from a certain metal surface. What is the longest wavelength of
light (nm) that can be used to eject electrons from the surface of this metal via the photoelectric
effect?
I'd appreciate it if someone could explain how to do this because I have a test tomorrow and don't know where to start. Thanks!
Well, we're talking about the photoelectric effect here, which is a pretty "bright" topic, if you catch my drift. So, to figure out the longest wavelength of light that can eject electrons from the metal surface, we need to bring some energy into the equation.
The energy of a photon (a particle of light) is given by the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 J⋅s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of light.
Now, if we want to eject electrons from the metal, we need to provide enough energy to overcome the work function of the metal, which in this case is 254 kJ/mol. But don't worry, we'll convert it to joules per particle!
To convert from kJ/mol to J/particle, divide by Avogadro's constant (6.022 x 10^23 particles/mol). So the work function per particle is 254,000 J/6.022 x 10^23 particles.
Now, let's plug it all in! Remember, we're looking for the longest wavelength, so we want the minimum energy.
The minimum energy required to eject an electron is the work function, so E = 254,000 J / 6.022 x 10^23 particles.
Now we set that equal to the energy of a photon, E = hc/λ.
Combining the equations, we have 254,000 J / 6.022 x 10^23 particles = hc/λ.
Now, we can solve for λ by rearranging the equation to get λ = hc / (254,000 J / 6.022 x 10^23 particles).
Crunching the numbers, you should get the longest wavelength of light (in nm) that can be used to eject electrons from the metal surface.
Good luck! And remember, if the calculations start to get you down, just tell a physics joke. It might not improve your grades, but at least it'll lighten the mood!
To determine the longest wavelength of light that can be used to eject electrons from a metal surface via the photoelectric effect, you can use the equation:
Energy of a photon = Planck's constant (h) × Frequency of light (v)
The energy required to eject an electron from the metal surface is given as 254 kJ/mol. To convert this into joules per photon, we need to divide by Avogadro's number (6.022 × 10^23) to get the energy per electron:
Energy per electron = (254 kJ/mol) / (6.022 × 10^23) = (254 × 10^3 J / mol) / (6.022 × 10^23) = 4.216 × 10^-19 J
Next, we rearrange the equation to solve for frequency:
Frequency of light (v) = Energy per electron / Planck's constant (h)
Now, we substitute the known values:
v = (4.216 × 10^-19 J) / (6.626 × 10^-34 J∙s)
v = 6.36 × 10^14 Hz
To find the longest wavelength, we use the relation between frequency and wavelength:
v = speed of light (c) / wavelength (λ)
We rearrange the equation to solve for wavelength:
wavelength (λ) = speed of light (c) / frequency of light (v)
Substituting the known values:
λ = (3 × 10^8 m/s) / (6.36 × 10^14 Hz)
λ ≈ 4.72 × 10^-7 m
Finally, we convert the wavelength to nanometers:
λ = (4.72 × 10^-7 m) × (10^9 nm / 1 m)
λ ≈ 472 nm
Therefore, the longest wavelength of light that can be used to eject electrons from the metal surface is approximately 472 nm.
To find the longest wavelength of light that can be used to eject electrons from the surface of the metal, we need to use the equation for the photoelectric effect:
E = hv
where E is the energy of a photon, h is the Planck constant (6.626 × 10^-34 J·s), and v is the frequency of the light.
To find the wavelength, we can use the relation between frequency and wavelength:
c = νλ
where c is the speed of light (3 × 10^8 m/s), ν is the frequency, and λ is the wavelength.
First, we need to determine the energy of a photon that is required to eject electrons from the metal surface. This energy is given as 254 kJ/mol.
To convert kJ/mol to J/photon, we can divide by Avogadro's number (6.022 × 10^23):
Energy per photon = (254 kJ/mol) / (6.022 × 10^23 mol^-1)
Next, we can use the equation E = hv to calculate the frequency of the light:
Frequency = Energy per photon / Planck constant
Once we have the frequency, we can use the relation c = νλ to find the wavelength:
Wavelength = speed of light / Frequency
Make sure to convert the wavelength to nanometers (nm) by multiplying by 10^9.
Following these steps should help you find the answer to the problem. Good luck on your test!
(1.48 cg) + (0.347 g) .
Answer in units of g
254,000 J/mol x (1 mol/6.022 x 10^23) = energy/photon.
delta E = hf. h is Planck's constant, f is the frequency of the light.
Then c = f*w
c = speed of light in m/s. f is frequency in Hz, w is wavelength in meters.