Determine the longest wavelength of light required to remove an electron from a sample of potassium metal, if the binding energy for an electron in K is 1.76 × 103 kJ/mol.
isn't Planck's equation working?
Energy= plancksconstant*speedlight/wavelength
You will have to get energy per electron, or
energy= 1.76E3*1E3avagradros number to get energy in joules/electron
opps, division sign disappeared.
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energy= 1.76E3*1E3/ avagradros number to get energy in joules/electron
To determine the longest wavelength of light required to remove an electron from potassium (K), you can use the equation:
E = hc/λ
Where:
E is the binding energy for the electron in joules (J)
h is Planck's constant (6.63 × 10^-34 J s)
c is the speed of light (3.00 × 10^8 m/s)
λ is the wavelength of light (in meters)
First, let's convert the binding energy from kJ/mol to J using Avogadro's number:
Binding energy in J = (1.76 × 10^3 kJ/mol) / (6.022 × 10^23 mol^-1) = 2.92 × 10^-21 J
Now, we can rearrange the equation to solve for the wavelength:
λ = hc/E
Inserting the values:
λ = (6.63 × 10^-34 J s) * (3.00 × 10^8 m/s) / (2.92 × 10^-21 J)
Calculating:
λ = 6.82 × 10^-7 m
Therefore, the longest wavelength of light required to remove an electron from a sample of potassium metal is approximately 6.82 × 10^-7 meters or 682 nm.
To determine the longest wavelength of light required to remove an electron from a sample of potassium metal, we can use the equation:
E = hc/λ
Where:
E is the energy required to remove an electron from the metal (binding energy),
h is Planck's constant (6.63 × 10^(-34) J·s),
c is the speed of light (3.00 × 10^8 m/s),
and λ is the wavelength of light.
First, let's convert the binding energy from kJ/mol to J:
Binding energy = 1.76 × 10^3 kJ/mol * (1000 J/1 kJ) = 1.76 × 10^6 J/mol
Next, we need to convert the energy per mole to energy per electron by dividing by Avogadro's number (6.022 × 10^23 electrons/mol):
Energy per electron = 1.76 × 10^6 J/mol / (6.022 × 10^23 electrons/mol) = 2.92 × 10^(-18) J/electron
Now, we can rearrange the equation to solve for the wavelength:
λ = hc / E
Plugging in the values:
λ = (6.63 × 10^(-34) J·s * 3.00 × 10^8 m/s) / 2.92 × 10^(-18) J/electron
Simplifying:
λ = 2.27 × 10^(-6) m
Therefore, the longest wavelength of light required to remove an electron from the potassium metal sample is approximately 2.27 × 10^(-6) meters.