If you put 120 volts of electricity through a pickle, the pickle will smoke and start glowing orange-yellow. The light is emitted because sodium ions in the pickle become excited; their return to the ground state results in light emission. b. What is the energy of 1.00 mol of these photons? (A mole of photons is called an Einstein.)

Verified step by step guidance

1. Identify the wavelength or frequency of the light emitted by the sodium ions. The orange-yellow light corresponds to a specific wavelength, typically around 589 nm for sodium.
2. Use the speed of light equation, \( c = \lambda \nu \), to find the frequency (\( \nu \)) if you have the wavelength (\( \lambda \)). Here, \( c \) is the speed of light, approximately \( 3.00 \times 10^8 \) m/s.
3. Calculate the energy of a single photon using the equation \( E = h \nu \), where \( h \) is Planck's constant, approximately \( 6.626 \times 10^{-34} \) J\cdot s.
4. Convert the energy of a single photon to the energy of 1 mole of photons (an Einstein) by multiplying the energy of one photon by Avogadro's number, \( 6.022 \times 10^{23} \) mol\(^{-1}\).
5. Express the final energy in joules per mole, which represents the energy of 1.00 mol of these photons.

Key Concepts

Photon Energy

Photon energy is the energy carried by a single photon, which can be calculated using the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν (nu) is the frequency of the light. This relationship shows that higher frequency light has more energy, which is relevant when considering the light emitted by excited sodium ions in the pickle.

Moles and Avogadro's Number

A mole is a unit in chemistry that represents 6.022 x 10^23 entities, known as Avogadro's number. When discussing energy in terms of moles of photons, it is essential to understand that 1 mole of photons contains this fixed number of photons, allowing for the calculation of total energy by multiplying the energy of a single photon by Avogadro's number.

Excitation and Emission of Electrons

When sodium ions in the pickle are exposed to electricity, their electrons absorb energy and move to a higher energy level, a state known as excitation. When these electrons return to their ground state, they release energy in the form of light. This process is fundamental to understanding how the glowing effect occurs in the pickle when subjected to high voltage.