1) Calculate the energy. in joules, of a photon of wavelength 1.250x 10^3 nm
2) If 3.011x 10^23 molecules have a mass of 20.04 grams, what is the molar mass of the substance?
Is it 40.07g/mol?
3) 47.5g of Boron contains __________ atoms of B?
Is it 2.65x10^24
4) What is the wavelength in meters, of a radio wave of frequency 2.8 x 10^18 1/s?
A. E/photon = hc/wavelength.
wavelength = 1.350E-9 m
B. I obtained 40.08 using 6.022E23 for Avogadro's number.
C. looks ok to me.
D. c = freq x wavelgnth
A. is wrong that is not one of the answers. I have calculated 1.5912 X 10^-28
but the only near answer is 1.591 x 10^-19
1) To calculate the energy of a photon, you can use the formula:
E = hc/λ
Where:
E is the energy of the photon,
h is Planck's constant (6.626 x 10^-34 J.s),
c is the speed of light in a vacuum (3.0 x 10^8 m/s),
λ is the wavelength of the photon.
First, we need to convert the given wavelength from nanometers (nm) to meters (m). Since 1 nm = 1 x 10^-9 m, the wavelength becomes:
λ = 1.250 x 10^3 nm = 1.250 x 10^-6 m
Now, we can plug these values into the formula to find the energy of the photon:
E = (6.626 x 10^-34 J.s) * (3.0 x 10^8 m/s) / (1.250 x 10^-6 m)
By calculating this expression, you will find the energy of the photon in joules.
2) To find the molar mass of a substance, you can use the relationship between the number of molecules and the mass.
The molar mass (M) is calculated by dividing the mass (m) of a substance by the number of moles (n) of that substance:
M = m/n
First, we need to find the number of moles. Given that 3.011 x 10^23 molecules have a mass of 20.04 grams, we can use Avogadro's number (6.022 x 10^23) to find the number of moles:
n = (3.011 x 10^23 molecules) / (6.022 x 10^23 molecules/mol)
Now, we can plug in the mass and number of moles into the molar mass formula to find the molar mass of the substance:
M = (20.04 grams) / (n moles)
By calculating this expression, you will find the molar mass of the substance in grams per mole (g/mol).
3) To determine the number of atoms in a given mass of a substance, you need to use the concept of moles.
The number of moles (n) can be calculated using the formula:
n = m / M
Where:
n is the number of moles,
m is the mass of the substance, and
M is the molar mass of the substance.
In this case, you are given the mass of Boron as 47.5 grams. To find the number of atoms of Boron, you need to know the molar mass of Boron (M). Since the atomic mass of Boron is approximately 10.81 grams/mole, the molar mass of Boron is 10.81 g/mol.
Now, plug in the values into the formula:
n = (47.5 grams) / (10.81 g/mol)
By calculating this expression, you will find the number of moles of Boron. Since one mole contains Avogadro's number (6.022 x 10^23) of atoms, you can multiply the number of moles by Avogadro's number to find the number of atoms.
Number of atoms = (number of moles) * (6.022 x 10^23)
4) To find the wavelength of a radio wave, you can use the formula:
c = λf
Where:
c is the speed of light in a vacuum (3.0 x 10^8 m/s),
λ is the wavelength of the radio wave,
f is the frequency of the radio wave.
Rearranging the formula to solve for wavelength gives:
λ = c/f
Given a radio wave frequency of 2.8 x 10^18 1/s, you can plug this value into the formula to find the wavelength of the radio wave:
λ = (3.0 x 10^8 m/s) / (2.8 x 10^18 1/s)
By calculating this expression, you will find the wavelength of the radio wave in meters.