Question

In an atom, an electron is moving with a speed of 600 m/sec with an accuracy of 0.005%. Certainty with which the position of the electron can be located is:

(h = 6.6 $\times$ ${10}^{-34}$ kg $m^3$ $s^{-1}$, mass of electron $m_e$ = 9.1 $\times$ ${10}^{-31}$ kg)

• A. 1.52 $\times$ ${10}^{-4}$ m
• B. 5.1 $\times$ ${10}^{-4}$ m
• C. 1.92 $\times$ ${10}^{-3}$ m
• D. 3.84 $\times$ ${10}^{-4}$ m

Answer 1

The correct option is C

1.92 $\times$ ${10}^{-3}$ m

From Heisenberg Uncertainty Principle, we know

$△$p $\times$ $△$x $\ge$ $\frac{h}{4\pi }$

$\Rightarrow$ $△$v $\times$ $△$x $\ge$ $\frac{h}{4\pi \times m}$

Now,

Uncertainty in velocity = $\frac{0.005}{100}$ $\times$ 600 = 0.03

Uncertainty in postition of electrons i.e, $△$ x ,may be calculate as ,

$△$x $\ge$ $\frac{h}{4\pi m△v}$

$\ge$ $\frac{6.626\times {10}^{-34}}{4\times 3.14\times 9.1\times {10}^{-31}\times 0.03}$

$\ge$ 1.92 $\times$ ${10}^{-3}$ m