1.Infrared radiation has wavelengths ranging

from about 800 nm to 1 mm. What is the
frequency of radiation of wavelength 970 nm?
Answer in units of s−1
.

2.Microwaves, such as those used for radar and
to heat food in a microwave oven, have wavelengths
greater than about 3 mm. What
is the frequency of radiation of wavelength
4.75 mm?
Answer in units of s−1
.

3.Sodium vapor lamps, used for public lighting,
emit yellow light of wavelength 560 nm. How
much energy is emitted by an excited sodium
atom when it generates a photon?
Answer in units of J.

4.How much energy is emitted by 45.8 mg of
sodium atoms emitting light at this wavelength?
Answer in units of J.

5.How much energy is emitted by 1 mol of
sodium ions emitting light at this wavelength?
Answer in units of kJ.

1.Infrared radiation has wavelengths ranging

from about 800 nm to 1 mm. What is the
frequency of radiation of wavelength 970 nm?
Answer in units of s−1

Convert nm to m and use c = f*w.
c is speed of light in m/s, solve for f(requency) and substitute for w(avelength).<?b>

2.Microwaves, such as those used for radar and
to heat food in a microwave oven, have wavelengths
greater than about 3 mm. What
is the frequency of radiation of wavelength
4.75 mm?
Answer in units of s−1

same procedure as #1.

3.Sodium vapor lamps, used for public lighting,
emit yellow light of wavelength 560 nm. How
much energy is emitted by an excited sodium
atom when it generates a photon?
Answer in units of J.

E = hc/wavelength

4.How much energy is emitted by 45.8 mg of
sodium atoms emitting light at this wavelength?
Answer in units of J.

mols Na = grams/atomic mass = ? mols.
E = hc/wavelength. That gives E in joules/1 atom. That x 6.02E23 = joules/1 mol. That x # moles from above = total E.


5.How much energy is emitted by 1 mol of
sodium ions emitting light at this wavelength?
Answer in units of kJ.

See problem 4.

3.43

1. The formula to calculate the frequency of radiation is given by:

frequency = speed of light / wavelength

Given that the wavelength is 970 nm (nanometers), which is equivalent to 970 x 10^-9 meters, and the speed of light is approximately 3.00 x 10^8 meters per second, we can substitute these values into the formula:

frequency = (3.00 x 10^8 m/s) / (970 x 10^-9 m)
= 3.09 x 10^14 s^-1

Therefore, the frequency of radiation with a wavelength of 970 nm is approximately 3.09 x 10^14 s^-1.

2. Using the same formula as in the previous question:

frequency = (3.00 x 10^8 m/s) / (4.75 x 10^-3 m)
= 6.32 x 10^10 s^-1

Therefore, the frequency of radiation with a wavelength of 4.75 mm is approximately 6.32 x 10^10 s^-1.

3. To calculate the energy emitted by a photon, we can use the formula:

energy = Planck's constant x frequency

Given that the wavelength of yellow light emitted by a sodium atom is 560 nm (or 560 x 10^-9 meters), we can determine the frequency using the formula from question 1:

frequency = (3.00 x 10^8 m/s) / (560 x 10^-9 m)
= 5.36 x 10^14 s^-1

Using Planck's constant (h = 6.63 x 10^-34 J·s):

energy = (6.63 x 10^-34 J·s) x (5.36 x 10^14 s^-1)
= 3.55 x 10^-19 J

Therefore, the energy emitted by an excited sodium atom when generating a photon of yellow light with a wavelength of 560 nm is approximately 3.55 x 10^-19 J.

4. To calculate the energy emitted by 45.8 mg of sodium atoms, we need to convert the mass into the number of sodium atoms using the molar mass of sodium (22.99 g/mol):

moles of sodium = mass (in grams) / molar mass
= 45.8 mg / (22.99 g/mol)
= 1.991 x 10^-3 mol

Since each sodium atom emits energy when generating a photon, the total energy emitted is equal to the energy per atom multiplied by the number of atoms:

total energy = energy per atom x number of atoms
= (3.55 x 10^-19 J) x (1.991 x 10^-3 mol x 6.022 x 10^23 atoms/mol)
= 4.04 x 10^5 J

Therefore, 45.8 mg of sodium atoms emitting light at a wavelength of 560 nm emit approximately 4.04 x 10^5 J of energy.

5. To calculate the energy emitted by 1 mol of sodium ions, we can use the Avogadro constant (6.022 x 10^23 ions/mol). Multiplying the energy per atom (from question 3) by the number of atoms in a mol:

total energy = energy per atom x number of atoms (in 1 mol)
= (3.55 x 10^-19 J) x (6.022 x 10^23 ions/mol)
= 2.14 x 10^5 J

Since the question asks for the answer in kJ, we can convert the answer:

total energy = 2.14 x 10^5 J = 214 kJ

Therefore, 1 mol of sodium ions emitting light at a wavelength of 560 nm emits approximately 214 kJ of energy.

1. To find the frequency of radiation given the wavelength, you can use the formula:

frequency (ν) = speed of light (c) / wavelength (λ)

The speed of light is approximately 3.00 x 10^8 m/s or 3.00 x 10^17 nm/s.

Converting 970 nm to meters:
970 nm = 970 x 10^(-9) m

Using the formula:
ν = (3.00 x 10^17 nm/s) / (970 x 10^(-9) m)

Calculating the frequency:
ν ≈ 3.09 x 10^14 s^(-1)

Answer: The frequency of radiation with a wavelength of 970 nm is approximately 3.09 x 10^14 s^(-1).

2. Similarly, to find the frequency of radiation given the wavelength, we use the formula mentioned above:

ν = (3.00 x 10^17 nm/s) / (4.75 x 10^(-3) m)

Calculating the frequency:
ν ≈ 6.32 x 10^10 s^(-1)

Answer: The frequency of radiation with a wavelength of 4.75 mm is approximately 6.32 x 10^10 s^(-1).

3. To determine the energy emitted by an excited sodium atom when it generates a photon, we can use the equation:

energy (E) = Planck's constant (h) * frequency (ν)

where Planck's constant is approximately 6.626 x 10^(-34) J·s.

First, we need to find the frequency using the same formula as above:

ν = (3.00 x 10^17 nm/s) / (560 x 10^(-9) m)

Calculating the frequency:
ν ≈ 5.36 x 10^14 s^(-1)

Now, we can calculate the energy:

E = (6.626 x 10^(-34) J·s) * (5.36 x 10^14 s^(-1))

Calculating the energy:
E ≈ 3.55 x 10^(-19) J

Answer: An excited sodium atom emits approximately 3.55 x 10^(-19) J of energy when it generates a photon with a wavelength of 560 nm.

4. To calculate the energy emitted by 45.8 mg of sodium atoms emitting light at a wavelength of 560 nm, we need to convert mass to moles and then use the formula for energy mentioned in the previous answer.

First, we convert the mass of sodium from milligrams to kilograms:
45.8 mg = 45.8 x 10^(-6) kg

Next, we calculate the number of moles of sodium using its molar mass, which is approximately 22.99 g/mol:
moles = mass (kg) / molar mass (g/mol)
moles ≈ (45.8 x 10^(-6) kg) / (22.99 g/mol)

Now, we can multiply the number of moles by Avogadro's constant to obtain the number of sodium atoms:
number of atoms = moles * Avogadro's constant

Finally, we can calculate the energy emitted by the sodium atoms using the formula mentioned earlier:

E = (number of atoms) * (energy per atom)

Answer: The energy emitted by 45.8 mg of sodium atoms emitting light at a wavelength of 560 nm would depend on the number of atoms present and the energy per atom, which requires further calculations.

5. To find the energy emitted by 1 mol of sodium ions emitting light at a wavelength of 560 nm, we can follow a similar approach as in the previous answer.

We start by calculating the number of sodium ions in 1 mol:

number of ions = Avogadro's constant

Next, we calculate the energy emitted by one sodium ion using the formula mentioned above:

E = (6.626 x 10^(-34) J·s) * (5.36 x 10^14 s^(-1))

Now, we can calculate the total energy emitted by 1 mol of sodium ions:

total energy = (number of ions) * (energy per ion)

Since the molar mass of sodium is approximately 22.99 g/mol, we can use the conversion factor:

(number of ions) = (Avogadro's constant) * (molar mass of sodium)

Finally, we convert the energy from joules to kilojoules by dividing by 1000:

energy in kJ = (total energy) / 1000

Answer: The energy emitted by 1 mol of sodium ions emitting light at a wavelength of 560 nm would depend on the number of ions present and the energy per ion, which requires further calculations.