The wavelength of light from the spectral emission line of sodium is 589 nm. The kinetic energy at which a neutron would have the same de Broglie wavelength is

Question

The wavelength of light from the spectral emission line of sodium is 589 nm. The kinetic energy at which a neutron would have the same de Broglie wavelength is (A) 3.81 × 10-28 J (B) 3.81 × 10-25 J (C) 4.81 × 10-28 J (D) 4.81 × 10-30 J

Tardigrade Admin · Accepted Answer

Given, wavelength of light =589 nm =589 × 10-9 m Mass of electron m e =9.1 × 10-31 kg Mass of neutron m n =1.67 × 10-27 kg Planck's constant h =6.62 × 10-34 J - s Kinetic energy of neutron KE n =( h 2/2 λ2 m n ) =((6.63 × 10-34)2/2 ×(589 × 10-9)2 × 1.66 × 10-27) =3.81 × 10-28 J

Q. The wavelength of light from the spectral emission line of sodium is $589 nm$ . The kinetic energy at which a neutron would have the same de Broglie wavelength is

$3.81 \times 1 0^{- 28} J$

$3.81 \times 1 0^{- 25} J$

$4.81 \times 1 0^{- 28} J$

$4.81 \times 1 0^{- 30} J$

Q. The wavelength of light from the spectral emission line of sodium is 589nm. The kinetic energy at which a neutron would have the same de Broglie wavelength is

3.81×10−28J

3.81×10−25J

4.81×10−28J

4.81×10−30J

Given, wavelength of light =589nm=589×10−9m Mass of electron me​=9.1×10−31kg Mass of neutron mn​=1.67×10−27kg Planck's constant h=6.62×10−34J−s Kinetic energy of neutron KEn​=2λ2mn​h2​ =2×(589×10−9)2×1.66×10−27(6.63×10−34)2​ =3.81×10−28J

Q. The wavelength of light from the spectral emission line of sodium is $589 nm$ . The kinetic energy at which a neutron would have the same de Broglie wavelength is

$3.81 \times 1 0^{- 28} J$

$3.81 \times 1 0^{- 25} J$

$4.81 \times 1 0^{- 28} J$

$4.81 \times 1 0^{- 30} J$