Question

what is the length of a box in which the minimum energy of an electron is 1.5*10^-18 J?

Answer 1

Answer:

L=2*10^-10m

Explanation:

we need to evaluate for a minimum energy:

Planck constant=  h = 6,62607015 ×10 -34 kg⋅m2⋅s−1

1.5*10^-18J = 10eV

En=  n^2h^2 /  8mL^2

for n=1 (minimum energy)

E1=  h^2 /  8mL^2

so...

L^2= h^2/(8mE1)

L^2= (6.63*10^-34)^2 / [ 8(9.11*10^-31 )*(1.5*10^-18J )]

L^2= 4.02*10^-20

L= 2*10^-10 m

Answer 2

The length of the box in which the value of minimum energy of an electron is 1.5*10^-18 J is,

$l=2\times10^{-10}\rm \; m$

What is kinetic energy?

Kinetic energy is a type of energy, which a body is posses due to its motion. The kinetic energy of the electron can be given as,

$E_n=\dfrac{n^2h}{8ml^2}$

For ground level,

$E_1=\dfrac{(1)^2h^2}{8ml^2}\\E_{min}=\dfrac{h^2}{8ml^2}$

The minimum energy of an electron is $1.5\times10^{-18} \rm J$. As the value of plank constant is $6.63\times10^{-34}\rm m^2kg/s$ and the mass of an electron is $9.1\times10^{-31}\rm kg$.

Put the values in the above formula as,

$1.5\times10^{-18} =\dfrac{(6.63\times10^{-34})^2}{8(9.1\times10^{-31})l^2}$

Solve this equation to get the value of length, we get,

$l=2\times10^{-10}\rm \; m$

Hence, the length of the box in which the value of minimum energy of an electron is 1.5*10^-18 J is,

$l=2\times10^{-10}\rm \; m$

Learn more about the kinetic energy here;

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