The binding energy of electrons in a metal is 194 kJ/mol.
Find the threshold frequency of the metal.
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The heat of fusion of ice is 6.00 kJ/mol.
Find the number of photons of wavelength = 6.78×10^−6 m that must be absorbed to melt 6.80 g of ice.
To find the threshold frequency of the metal, we can use the equation:
Binding energy of electrons = threshold frequency × Planck's constant
The binding energy of electrons in a metal is given as 194 kJ/mol.
Let's convert this to joules per particle:
1 kJ/mol = 1 kJ / (6.022 × 10^23 particles)
194 kJ/mol = 194 kJ / (6.022 × 10^23 particles)
Now, let's convert this to joules per electron:
1 particle → 1 electron
194 kJ / (6.022 × 10^23 particles) = 194 kJ / (6.022 × 10^23 electrons)
Next, we need to convert the binding energy from joules to electron volts (eV) since threshold frequencies are typically given in eV:
1 eV = 1.602 × 10^−19 J
Thus, we have:
194 kJ / (6.022 × 10^23 electrons) = (194 × 10^3 J) / (6.022 × 10^23 electrons) = (194 × 10^3 J) / (6.022 × 10^23 electrons) × (1 eV / 1.602 × 10^−19 J)
Now, divide the obtained value by the Planck's constant (h) to get the threshold frequency:
threshold frequency = ((194 × 10^3 J) / (6.022 × 10^23 electrons) × (1 eV / 1.602 × 10^−19 J)) / h
Planck's constant (h) is approximately 6.626 × 10^−34 J·s.
Now, you can calculate the threshold frequency using the given values and the formula above.