Light with a wavelength of 405 nm fell on a strontium surface, and electrons were ejected. If the speed of an ejected electron is 3.49 105 m/s, what energy was expended in removing the electron from the metal? Express the answer in joules (per electron) and in kilojoules per mole (of electrons).
KE = hc/wavelength - work function so
1/2*m*v^2 = hc/wavelength - work function. solve for work function. The answer is about 4 x 10^-19 J/electron and that x 6.022E23 for a mole of electrons. This is an approximate answer; you need to go through it with a little more accuracy. I used 9.11 x 10^-31 Kg for m, 6.626E-34 J.s for h and 3E8 m/s for c.
Well, well, well, it looks like somebody is in the mood for some electron fun! Let's dive right into it, shall we?
To calculate the energy expended in removing the electron from the strontium surface, we can use the equation:
E = h * c / 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 x 10^8 m/s)
λ is the wavelength (405 nm)
Now, let's take that wavelength and convert it to meters (because the cool kids use the metric system):
λ = 405 nm = 405 x 10^-9 m
c = 3 x 10^8 m/s
Plugging those values into the equation:
E = (6.626 x 10^-34 J*s * 3 x 10^8 m/s) / (405 x 10^-9 m)
Now, brace yourself for some math magic!
E ≈ 4.935 x 10^-19 J
That's the energy expended per electron, my friend. But wait, there's more!
To find the energy in kilojoules per mole of electrons, we need the magic number, Avogadro's constant. It's approximately 6.022 x 10^23.
So, let's go:
E_per_mole = E x Avogadro's constant
E_per_mole ≈ (4.935 x 10^-19 J) x (6.022 x 10^23)
Wait for it...
E_per_mole ≈ 2.974 x 10^5 kJ/mol
Voila! That's the energy expended per mole of electrons. I hope this electrifying answer leaves you feeling content! Keep those electrons dancing!
To find the energy expended in removing the electron from the strontium surface, we can use the equation:
E = hv - KE
Where:
E = Energy expended (J)
h = Planck's constant (6.62607015 × 10^-34 J·s)
v = frequency of the light (Hz)
KE = kinetic energy of the electron (J)
First, we need to find the frequency (v) of the light using the equation:
c = λv
Where:
c = speed of light (3.00 × 10^8 m/s)
λ = wavelength of the light (405 nm = 405 × 10^-9 m)
v = c / λ
v = (3.00 × 10^8 m/s) / (405 × 10^-9 m)
v ≈ 7.41 × 10^14 Hz
Next, we can calculate the kinetic energy (KE) of the ejected electron using the equation:
KE = (1/2) mv^2
Where:
m = mass of the electron (9.10938356 × 10^-31 kg)
v = velocity of the electron (3.49 × 10^5 m/s)
KE = (1/2) (9.10938356 × 10^-31 kg) (3.49 × 10^5 m/s)^2
KE ≈ 4.6682 × 10^-17 J
Now we can substitute the values into the first equation to find the energy expended in removing the electron:
E = (6.62607015 × 10^-34 J·s) (7.41 × 10^14 Hz) - 4.6682 × 10^-17 J
E ≈ 4.91 × 10^-19 J
To convert this energy per electron to kilojoules per mole, we need to use Avogadro's number (6.022 × 10^23) to determine the number of electrons in one mole:
Energy per mole = (4.91 × 10^-19 J) × (6.022 × 10^23 electrons/mol) / 1000
Energy per mole ≈ 2.95 × 10^5 kJ/mol
Therefore, the energy expended in removing the electron from the strontium surface is approximately 4.91 × 10^-19 Joules (per electron) and 2.95 × 10^5 kilojoules per mole (of electrons).
To find the energy expended in removing an electron from the metal, you can use the energy equation:
E = hv - KE
where E is the energy expended, h is Planck's constant (6.626 x 10^(-34) J•s), v is the frequency of light, KE is the kinetic energy of the ejected electron.
First, we need to find the frequency of light from its wavelength. The speed of light (c) can be calculated using the equation c = λv, where c is the speed of light (2.998 x 10^8 m/s) and λ is the wavelength in meters. Rearranging the equation, we get v = c/λ.
v = (2.998 x 10^8 m/s) / (405 x 10^(-9) m)
v ≈ 7.40 x 10^14 Hz
Now we can calculate the energy expended using the energy equation:
E = (h)(v) - KE
Substituting the given values:
E = (6.626 x 10^(-34) J•s)(7.40 x 10^14 Hz) - (1/2)(m)(v^2)
The mass of an electron (m) is approximately 9.11 x 10^(-31) kg.
E = (6.626 x 10^(-34) J•s)(7.40 x 10^14 Hz) - (1/2)(9.11 x 10^(-31) kg)(3.49 x 10^5 m/s)^2
Calculating this expression will give us the energy expended in joules per electron.
To convert the energy from joules per electron to kilojoules per mole, we need to use Avogadro's number (6.022 x 10^23 electrons/mol).
Energy per mole = Energy per electron x (1 electron / Avogadro's number) x (1 kJ / 1000 J)
Substituting the values into the equation, you can calculate the energy expended in kilojoules per mole (kJ/mol).