It takes 208.4 kJ of energy to remove one mol of electrons from the atoms on the surface of rubidium metal. If rubidium metal metal is irradiated with 254-nm light, what is the maximum kinetic energy the released electrons can have?
208,400 J/mol x (1/6.02E23) = ? work function.
E of photon = hc/wavlength = 6.626E-34*3E8/254E-9 = x
Take the difference between x and ? above and that is the maximum energy of an ejected electron which is KE = 1/2 mv2. Then solve for v in m/s.
To find the maximum kinetic energy of the released electrons, we can use the equation:
Energy of light = Binding energy + Kinetic energy
First, we need to calculate the energy of light using the equation:
Energy of light = (Planck's constant * speed of light) / wavelength
Let's plug in the values:
Energy of light = (6.626 × 10^-34 J·s * 3.00 × 10^8 m/s) / (254 × 10^-9 m)
Now, let's calculate the energy of light:
Energy of light = (1.58 × 10^-25 J)
Next, we can calculate the maximum kinetic energy by subtracting the binding energy from the energy of light:
Maximum Kinetic Energy = Energy of light - Binding energy
Let's calculate the maximum kinetic energy:
Maximum Kinetic Energy = (1.58 × 10^-25 J) - (208.4 kJ * 10^3 J/kJ * 1 mol^-1)
Note: We need to convert kJ to J and divide by the Avogadro's number (6.022 × 10^23 mol^-1) to convert from per mole to per electron.
Maximum Kinetic Energy = (1.58 × 10^-25 J) - (208.4 × 10^3 J * 10^3 J/kJ / 6.022 × 10^23 mol^-1)
Now, let's calculate the maximum kinetic energy:
Maximum Kinetic Energy = (1.58 × 10^-25 J) - (34.59 × 10^-19 J)
Finally, let's evaluate the maximum kinetic energy:
Maximum Kinetic Energy ≈ -34 × 10^-19 J
Note: The negative sign indicates that for the given wavelength of light (254 nm), the energy is not sufficient to remove an electron from the rubidium metal surface.
To find the maximum kinetic energy of the released electrons, we need to equate the energy of the incident light (254-nm) to the energy required to remove one mole of electrons from the surface of rubidium metal.
First, let's convert the wavelength of the light to energy using the equation:
E = hc / λ
Where:
E is the energy of the light
h is Planck's constant (6.626 × 10^-34 J·s)
c is the speed of light (3.00 × 10^8 m/s)
λ is the wavelength of the light
Converting the wavelength to meters:
λ = 254 nm = 254 × 10^-9 m
Now, let's calculate the energy of the incident light:
E = (6.626 × 10^-34 J·s) × (3.00 × 10^8 m/s) / (254 × 10^-9 m)
Simplifying the expression:
E ≈ 7.77 × 10^-19 J
Since we know it takes 208.4 kJ (or 208.4 × 10^3 J) to remove one mole of electrons, we can calculate the maximum kinetic energy (KE) of the released electrons using the equation:
KE = E - ionization energy
KE = 7.77 × 10^-19 J - 208.4 × 10^3 J/mol
Now, we need to convert the ionization energy from J/mol to J to match the units:
KE = 7.77 × 10^-19 J - (208.4 × 10^3 J/mol × 6.02 × 10^23 mol^-1)
Simplifying the expression:
KE ≈ 7.77 × 10^-19 J - 1.253 × 10^5 J
Rounding to the appropriate number of significant figures:
KE ≈ -1.252 × 10^5 J
The maximum kinetic energy of the released electrons is approximately -1.252 × 10^5 J (rounded to the appropriate number of significant figures). Note that the negative sign indicates that energy was released in the process.