hi
can you please help me with this particular question?
thanks a lot
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The work function of a material refers to the minimum energy required to remove an electron from the material. Assume that the work function of gold is 4.90eV and that of cesium is 1.90eV. Calculate the maximum wavelength of light for the photoeclectric emission of electrons for gold and cesium.
h c/(min. wavelength) = e*(work function)
Solve for the minimum wavelength.
h is Planck's constant
Convert the work function (in volts) to energy units by multiplying by the electron charge, e.
To calculate the maximum wavelength of light for the photoelectric emission of electrons for gold and cesium, we can use the equation:
hc / λ = e * work function
Where:
λ = wavelength of light
h = Planck's constant (6.626 x 10^-34 J s)
c = speed of light (3.00 x 10^8 m/s)
e = charge of an electron (1.602 x 10^-19 C)
Work function is given in eV, so we need to convert it to Joules by multiplying it by the electron charge, e.
Let's calculate the maximum wavelength for gold first:
Work function of gold = 4.90 eV
Step 1: Convert work function to Joules
work function (gold) = 4.90 eV * (1.602 x 10^-19 C/eV)
= 7.845 x 10^-19 J
Step 2: Substitute the values into the equation and solve for λ
hc / λ = (1.602 x 10^-19 C) * (7.845 x 10^-19 J)
λ = (6.626 x 10^-34 J s * 3.00 x 10^8 m/s) / [(1.602 x 10^-19 C) * (7.845 x 10^-19 J)]
Now, let's calculate the maximum wavelength for cesium:
Work function of cesium = 1.90 eV
Step 1: Convert work function to Joules
work function (cesium) = 1.90 eV * (1.602 x 10^-19 C/eV)
= 3.0438 x 10^-19 J
Step 2: Substitute the values into the equation and solve for λ
hc / λ = (1.602 x 10^-19 C) * (3.0438 x 10^-19 J)
λ = (6.626 x 10^-34 J s * 3.00 x 10^8 m/s) / [(1.602 x 10^-19 C) * (3.0438 x 10^-19 J)]
By solving these equations, you will find the maximum wavelengths of light for the photoelectric emission of electrons for gold and cesium.
To calculate the maximum wavelength of light for the photoelectric emission of electrons for gold and cesium, you can use the equation:
hc/(minimum wavelength) = e * (work function)
where:
h is Planck's constant (6.626 x 10^-34 J·s or 4.136 x 10^-15 eV·s)
c is the speed of light (3.00 x 10^8 m/s)
e is the elementary charge (1.602 x 10^-19 C or 1 eV)
First, convert the work function of gold (4.90 eV) and cesium (1.90 eV) to energy units by multiplying by the electron charge:
Gold:
Work function = 4.90 eV * (1.602 x 10^-19 C/eV) = 7.8398 x 10^-19 J
Cesium:
Work function = 1.90 eV * (1.602 x 10^-19 C/eV) = 3.0438 x 10^-19 J
Next, rearrange the equation to solve for the minimum wavelength:
minimum wavelength = hc / (e * work function)
Substituting the values we have:
For gold:
minimum wavelength for gold = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (1.602 x 10^-19 C * 7.8398 x 10^-19 J)
For cesium:
minimum wavelength for cesium = (6.626 x 10^-34 J·s * 3.00 x 10^8 m/s) / (1.602 x 10^-19 C * 3.0438 x 10^-19 J)
Now, calculate the values:
minimum wavelength for gold = 2.538 x 10^-7 m (or 253.8 nm)
minimum wavelength for cesium = 6.718 x 10^-7 m (or 671.8 nm)
Therefore, the maximum wavelengths of light for the photoelectric emission of electrons are approximately 253.8 nm for gold and 671.8 nm for cesium.