If the energy required to remove an electron from sodium is #8.23*10^-19# #J#,, what frequency of light will cause sodium to ionize?

Question

Naomi Aronson · Accepted Answer

The frequency is #1.25 × 10^15color(white)(l) "Hz"#.

The formula for the energy of a quantum of light is #color(blue)(bar(ul(|color(white)(a/a) E = hfcolor(white)(a/a)|)))" "# where #E# = energy #h# = Planck's constant #f# = frequency We can rearrange the formula to get #f = E/h# ∴ #f = (8.23 × 10^"-19" color(red)(cancel(color(black)("J"))))/(6.626 × 10^"-34" color(red)(cancel(color(black)("J")))·"s") = 1.25 × 10^15color(white)(l) "s"^"-1" = 1.25 × 10^15color(white)(l) "Hz"#

Serenity Allen · Answer

undefined The frequency of light required to ionize sodium can be calculated using the formula:

$$ E = h \cdot f $$

Where:
- $ E $ is the energy required to remove an electron (given as $ 8.23 \times 10^{-19} $ J).
- $ h $ is Planck's constant ($ 6.626 \times 10^{-34} $ J·s).
- $ f $ is the frequency of light (in Hz).

Rearranging the formula to solve for $ f $:

$$ f = \frac{E}{h} $$

Substituting the given values:

$$ f = \frac{8.23 \times 10^{-19} \, J}{6.626 \times 10^{-34} \, J \cdot s} $$

$$ f \approx 1.24 \times 10^{15} \, Hz $$

Therefore, the frequency of light required to ionize sodium is approximately $ 1.24 \times 10^{15} $ Hz.