Please help me break this problem down.. Thanks lot.
Light with a wavelength of 425 nm fell on a potassium surface, and electrons were ejected at a speed of 4.88 X 10^5 m/s. What energy was expended in removing an electron from the metal? Express the answer in joules (per electron) and in kilojoules per mole ( of electrons).
energy of the photon = hc/lambda.
You know h,c, and lambda. Be sure to change lambda to meters.
KE of the ejected electron
= 1/2 mv2. Remember to use kg for mass of electron.
Energy expended is the difference of the two. This will be per electron ejected and it will be in joules. Multiply that by 6.02 x 10^23 to change to per mol of electrons.
Sure! Let's break down the problem step by step:
Step 1: Identify the given information:
- The wavelength of light: 425 nm
- The speed of the ejected electron: 4.88 x 10^5 m/s
Step 2: Determine the frequency of the light:
The frequency (ν) of a wave can be calculated using the equation: c = λν, where c is the speed of light (approximately 3 x 10^8 m/s) and λ is the wavelength. Rearranging the formula, we get: ν = c/λ
ν = (3 x 10^8 m/s) / (425 x 10^-9 m)
ν ≈ 7.06 x 10^14 Hz
Step 3: Calculate the energy of a single photon:
The energy (E) of a photon is given by the equation: E = hν, where h is Planck's constant (approximately 6.626 x 10^-34 J·s).
E = (6.626 x 10^-34 J·s) x (7.06 x 10^14 Hz)
E ≈ 4.67 x 10^-19 J
Step 4: Calculate the energy expended in removing an electron:
The energy expended to remove an electron from the metal is equal to the energy of a single photon.
Energy per electron = 4.67 x 10^-19 J
Step 5: Convert the energy per electron to kJ/mol:
To convert from joules per electron to kilojoules per mole, we need to use Avogadro's number (approximately 6.022 x 10^23 electrons per mole).
Energy per mole = (Energy per electron) x (1 mole / 6.022 x 10^23 electrons)
Energy per mole = (4.67 x 10^-19 J) x (1 mole / 6.022 x 10^23 electrons)
Energy per mole ≈ 7.75 x 10^4 kJ/mol
So, the energy expended in removing an electron from the metal is approximately 4.67 x 10^-19 joules per electron and 7.75 x 10^4 kilojoules per mole of electrons.
To calculate the energy expended in removing an electron from the metal, we can use the equation:
E = hc/λ
Where:
E is the energy
h is the Planck's constant (6.626 x 10^-34 J⋅s)
c is the speed of light (3 x 10^8 m/s)
λ is the wavelength of light (425 nm = 425 x 10^-9 m)
First, let's convert the wavelength from nanometers to meters:
425 nm = 425 x 10^-9 m
Substituting the values into the equation:
E = (6.626 x 10^-34 J⋅s) x (3 x 10^8 m/s) / (425 x 10^-9 m)
Simplifying:
E = 1.98 x 10^-19 J
So, the energy expended in removing one electron from the metal is 1.98 x 10^-19 J.
To convert this energy to kilojoules per mole of electrons, we need to use Avogadro's number (6.022 x 10^23 mol^-1) to convert from per electron to per mole of electrons.
Multiplying the energy per electron by the number of electrons in one mole:
E_mole = (1.98 x 10^-19 J) x (6.022 x 10^23 mol^-1)
Simplifying:
E_mole = 1.19 x 10^5 J/mol
To convert it to kilojoules per mole, divide by 1000:
E_mole = 119 kJ/mol
So, the energy expended in removing one electron from the metal is 1.98 x 10^-19 J (per electron) and 119 kJ/mol (of electrons).