A source of monochromatic radiation of wavelength 400 nm provides 1000 J of energy in 10 seconds. When this radiation falls on the surface of sodium, x × 1020 electrons are ejected per second. Assume that wavelength 400 nm is sufficient for ejection of electron from the surface of sodium metal. The value of x is (Nearest integer) (h=6.626 × 10-34 JS)

Question

A source of monochromatic radiation of wavelength 400 nm provides 1000 J of energy in 10 seconds. When this radiation falls on the surface of sodium, x × 1020 electrons are ejected per second. Assume that wavelength 400 nm is sufficient for ejection of electron from the surface of sodium metal. The value of x is (Nearest integer) (h=6.626 × 10-34 JS) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Total energy provided by
Source per second

= \frac{1000}{10} = 100 J

Energy required to eject electron

= \frac{h c}{λ}

= \frac{6.626 \times 1 0 ^{- 34}}{400 \times 1 0 ^{- 9}} \times 3 \times 1 0^{8}

Number of electrons ejected

= \frac{100}{\frac{6.626 \times 1 0 ^{- 34} \times 3 \times 1 0 ^{8}}{400 \times 1 0 ^{- 9}}}

= \frac{400 \times 1 0 ^{- 7} \times 1 0 ^{26}}{6.626 \times 3}

= \frac{40 \times 1 0 ^{- 20}}{6.626 \times 3}

= 2.01 \times 1 0^{20}

Total energy provided by Source per second =101000​=100J Energy required to eject electron =λhc​ =400×10−96.626×10−34​×3×108 Number of electrons ejected =400×10−96.626×10−34×3×108​100​ =6.626×3400×10−7×1026​ =6.626×340×10−20​ =2.01×1020