The energy required to ionize sodium is 496 kJ/mol. What minimum frequency of light is required to ionize sodium?

검증된 단계별 안내

First, understand that ionization energy is the energy required to remove an electron from an atom or ion. In this case, it's the energy needed to ionize sodium.

Convert the ionization energy from kilojoules per mole (kJ/mol) to joules per mole (J/mol) by multiplying the given value by 1000, since 1 kJ = 1000 J.

Use the formula for the energy of a photon, which is given by \(E = h \nu\), where \(E\) is the energy, \(h\) is Planck's constant (\(6.626 \times 10^{-34}\) Js), and \(\nu\) is the frequency of the light.

Rearrange the formula to solve for the frequency, \(\nu = \frac{E}{h}\). Substitute the energy value you converted into joules per mole in step 2.

Since the energy provided is per mole, and Avogadro's number (\(6.022 \times 10^{23} \text{ mol}^{-1}\)) gives the number of particles per mole, divide the energy per photon by Avogadro's number to find the energy per photon, then use this value to find the frequency.

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주요 개념

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Ionization Energy

Ionization energy is the amount of energy needed to remove an electron from an atom or ion in its gaseous state. For sodium, this energy is quantified as 496 kJ/mol, indicating the energy required to ionize one mole of sodium atoms. Understanding this concept is crucial for determining the energy needed to overcome the attractive forces holding the electron to the nucleus.

Photon Energy

The energy of a photon is directly related to its frequency and 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 is essential for converting the ionization energy of sodium into the corresponding frequency of light required to provide that energy for ionization.

Planck's Constant

Planck's constant is a fundamental constant in quantum mechanics that relates the energy of a photon to its frequency. It is a key component in the equation E = hν, and its value is approximately 6.626 x 10^-34 J·s. Understanding Planck's constant is vital for calculating the minimum frequency of light needed to ionize sodium based on its ionization energy.