If an electron has an energy such that its de-Broglie wavelength is 5500 mathringA, then the energy value of that electron is (h=6.6 × 10-34 Js , m C =9.1 × 10-31 kg )

Question

If an electron has an energy such that its de-Broglie wavelength is 5500 mathringA, then the energy value of that electron is (h=6.6 × 10-34 Js , m C =9.1 × 10-31 kg ) (A) 8 × 10-20 J (B) 8 × 10-10 J (C) 8 J (D) 8 × 10-25 J

Tardigrade Admin · Accepted Answer

de-Broglie wavelength λ =(h/√2 m E) E =(1/2 m)((h/λ))2 =(1/2 × 9.1 × 10-31)((6.625 × 10-34/5.5 × 10-7))2 =(1/18.2 × 10-31) × 1.45 × 10-54 =8 × 10-25 J

Q. If an electron has an energy such that its de-Broglie wavelength is $5500 \overset{˚}{A}$ , then the energy value of that electron is
$(h = 6.6 \times 1 0^{- 34} J s, m_{C} = 9.1 \times 1 0^{- 31} k g)$

$8 \times 1 0^{- 20} J$

$8 \times 1 0^{- 10} J$

$8 J$

$8 \times 1 0^{- 25} J$

de-Broglie wavelength
$λ = \frac{h}{2 m E}$
$E = \frac{1}{2 m} (\frac{h}{λ})^{2}$
$= \frac{1}{2 \times 9.1 \times 1 0 ^{- 31}} (\frac{6.625 \times 1 0 ^{- 34}}{5.5 \times 1 0 ^{- 7}})^{2}$
$= \frac{1}{18.2 \times 1 0 ^{- 31}} \times 1.45 \times 1 0^{- 54}$
$= 8 \times 1 0^{- 25} J$

Q. If an electron has an energy such that its de-Broglie wavelength is 5500A˚, then the energy value of that electron is (h=6.6×10−34Js,mC​=9.1×10−31kg)

8×10−20J

8×10−10J

8J

8×10−25J