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Structure of Atom question

2011 · Shift 1 · Q9
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Structure of Atom question

2011 · Shift 1 · Q9

JEE AdvancedChemistryStructure of AtomNumerical+4 / −1
The work function ( φ ) of some metals is listed below. The number of metals which will show photoelectric effect when light of 300 nm wavelength falls on the metal is
Metal Li Na K Mg Cu Ag Fe Pt W
Ф (eV) 2.4 2.3 2.2 3.7 4.8 4.3 4.7 6.3 4.75
Numerical answer
View written solutionFree

Correct answer: 4

  1. Use the photoelectric condition

A metal will show photoelectric effect if the energy of the incident photon is at least equal to its work function:

hν≥ϕh\nu \ge \phihν≥ϕ

For light of wavelength λ=300 nm\lambda = 300\,\text{nm}λ=300nm, photon energy is

E=hcλE = \frac{hc}{\lambda}E=λhc​

Using the standard shortcut in electron-volts,

E(eV)=1240λ(nm)=1240300≈4.13 eVE(\text{eV}) = \frac{1240}{\lambda(\text{nm})} = \frac{1240}{300} \approx 4.13\,\text{eV}E(eV)=λ(nm)1240​=3001240​≈4.13eV

  1. Compare with each metal's work function

A metal emits photoelectrons if

ϕ≤4.13 eV\phi \le 4.13\,\text{eV}ϕ≤4.13eV

Given work functions:

  • Li: 2.42.42.4 eV ✅
  • Na: 2.32.32.3 eV ✅
  • K: 2.22.22.2 eV ✅
  • Mg: 3.73.73.7 eV ✅
  • Cu: 4.84.84.8 eV ❌
  • Ag: 4.34.34.3 eV ❌
  • Fe: 4.74.74.7 eV ❌
  • Pt: 6.36.36.3 eV ❌
  • W: 4.754.754.75 eV ❌
  1. Count the metals

The metals satisfying the condition are:

Li, Na, K, Mg\text{Li, Na, K, Mg}Li, Na, K, Mg

So the total number is

444

  1. Comparison with stored answer

Derived answer = 444

Stored correct answer = 444

They match.

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