CHEM Weekly Question 1-4

If the frequency of electromagnetic radiation is doubled, the energy is ____________.

• doubled

• halved

• unchanged

• tripled

Answer explanation

The energy of electromagnetic radiation is directly proportional to its frequency (E = hν). Therefore, if the frequency is doubled, the energy is also doubled. E is the energy of the photon, h is Planck’s constant, and v is the frequency of the photon.

If the wavelength is doubled the energy is ____________.

• halved

• doubled

• unchanged

• quadrupled

Answer explanation

Energy is inversely proportional to wavelength, as shown by E = (h * c) / λ, where E is energy in joules, h is Planck’s constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters. Doubling the wavelength results in halving the energy.

If the wavenumber is doubled, the energy is __________.

• doubled

• halved

• quadrupled

• unchanged

Answer explanation

The energy is directly proportional to the wavenumber, given by E = h x c x wavenumber, where E is energy in joules, h is Planck’s constant, and c is the speed of light (3.00 x 10^8 m/s). Doubling the wavenumber therefore doubles the energy.

The stretching frequency of a carbonyl (C=O) bond in a typical ketone is 5.15 × 10¹³ Hz. The vibrational energy of the molecule increases when light of this frequency is absorbed. What is the wavelength of this light in nanometres?

• 580 nm

• 583 nm

• 586 nm

• 589 nm

Answer explanation

The wavelength λ is calculated using λ = c / v, where c is the speed of light (3.00 × 10^8 m/s) and v is the frequency (5.15 × 10^13 Hz). This gives a wavelength of approximately 586 nm.

What is the wavelength of this light in micrometres if it is 586 nm

• 0.586 um

• 5.86 um

• 0.0586um

• 0.59um

Answer explanation

To convert 586 nm to micrometres, divide by 1000 (since 1 μm = 1000 nm), giving 0.586 μm.

Express the frequency of this light (586 nm) in wavenumbers

• 1 cm⁻¹

• 10 cm⁻¹

• 100 cm⁻¹

• 1000 cm⁻¹

Answer explanation

Wavenumber (in cm^-1) is calculated as wavenumber = v / c, where v is the frequency (5.15 × 10^13 Hz) and c is the speed of light in cm/s (3.00 × 10^10 cm/s). Dividing gives approximately 1000 cm^-1

What is the energy (in joules) of a single photon of light at this frequency?

• 3.3 x 10^-19 J

• 4.0 x 10^-19 J

• 5.5 x 10^-19 J

• 6.6 x 10^-19 J

Answer explanation

Energy E of a photon is calculated as E = h * v, where h is Planck’s constant (6.626 x 10^-34 J·s) and v is frequency (5.15 × 10^13 Hz), yielding approximately 6.6 x 10^-19 J.

What is the energy (in kilojoules) of one mole of photons at this frequency?

• 3.98 x 10^5 kJ

• 2.99 x 10^5 kJ

• 1.99 x 10^5 kJ

• 4.98 x 10^5 kJ

Answer explanation

The energy per mole of photons is calculated by multiplying the energy of a single photon by Avogadro’s number: E_mole = E_photon N_A, where E_photon is calculated from h v and N_A is Avogadro’s number (6.022 x 10^23 mol^-1). This yields approximately 2.99 x 10^5 kJ.

Into what region of the electromagnetic spectrum does this radiation fall?

• Radio Waves

• Microwaves

• Infrared

• Visible Light

Answer explanation

The frequency of 5.15 × 10^13 Hz falls within the infrared region of the electromagnetic spectrum, which lies between about 10^12 and 10^14 Hz.

A small amount of caffeine (194.19 g/mol) was dissolved in enough water to make 500.0 mL of solution. A 2.00-mL aliquot of this solution was then diluted to 100.0 mL. The absorbance of the second solution at 273 nm was 0.463 using a 1.000-cm cuvette. If the molar attenuation coefficient of caffeine at 273 nm is 9841 L mol⁻¹ cm⁻¹, what mass, in milligrams, of caffeine were used to make the original solution?

• 10.0 mg

• 20.0 mg

• 30.0 mg

• 40.0 mg

Answer explanation

Using the Beer-Lambert law A = ε c l to find concentration c, where A is absorbance (0.463), ε is the molar attenuation coefficient (9841 L mol^-1 cm^-1), and l is the path length (1.0 cm), we calculate c and backtrack through dilutions to find the original mass of caffeine, yielding 20.0 mg.