Question

A microscope using suitable photons is employed to locate an electron in an atom within a distance of 0.1A. What is the uncertainly involved in the measurement of its velocity ?
✯ᴘʟᴇᴀsᴇ ᴀɴsᴡᴇʀ ɪɴ ᴅᴇᴛᴀɪʟ
✯ᴜɴᴡᴀɴᴛᴇᴅ ᴀɴsᴡᴇʀs ᴏʀ ᴏɴᴇ ᴡᴏʀᴅ ᴀɴsᴡᴇʀs ᴡɪʟʟ ʙᴇ ᴅᴇʟᴇᴛᴇᴅ

Answer 1

Here's your answer in the given attachment.

value of h = 6.126×10^-34

mass of electron = 9.1 ×10^-31 kg

thanks

Answer 2

$\huge\bf{\color{indigo}GIVEN}$

• A microscope using suitable photons is employed to locate an electron in an atom within a distance of 0.1 A.

$\huge\bf\blue{TO\:FIND}$

• The uncertainty involved in the measurement of its velocity.

$\huge\bf\orange{SOLUTION}$

__________________________

$\bf{\underline{\color{cadetblue}CONCEPT}}$↓↓↓↓

Hᴇɪsᴇɴʙᴇʀɢ Uɴᴄᴇʀᴛᴀɪɴɪᴛʏ Pʀɪɴᴄɪᴘʟᴇ

Aᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜɪs ᴘʀɪɴᴄɪᴘʟᴇ, “it is impossible to measure simultaneously the position and momentum of a microscopic particle with absolute accuracy”.

[Nᴏᴛᴇ ➝ If one of them is measured with greater accuracy, the other becomes less accurate.]

$\red\bigstar\:\bf\purple{\triangle{x}\:.\:\triangle{p}\:\geq\:\dfrac{h}{4\pi}\:~~or~~\:\triangle{x}\:.\:\triangle{v}\:\geq\:\dfrac{h}{4\pi{m}}\:}$

$\bf\pink{Where,}$

• ∆x = Uncertainty in position.

• ∆p = Uncertainty in momentum.

• h = Planks Constant.

• m = mass of microscopic particle.

• ∆v = Uncertainty in velocity.

__________________________

$\huge\red\checkmark$ $\bf\purple{\triangle{x}\:.\:\triangle{v}\:\geq\:\dfrac{h}{4\pi{m}}\:}$

$\longmapsto\:\bf{\triangle{v}\:\geq\:\dfrac{h}{4\pi{m}\triangle{x}}\:}$

$\bf{\color{lime}We\:have,}$

• m = mass of electron $\bf\gray{=\:9.1\times{10^{-31}}\:kg}$

• h = $\bf\gray{6.626\times{10^{-34}}\:J.s}$

• π = $\bf\gray{3.14}$

• ∆x $\bf{=\:0.1\:A°\:\gray{=\:0.1\times{10^{-10}}\:m}}$

$\longmapsto\:\bf{\triangle{v}\:=\:\dfrac{6.626\times{10^{-34}}}{4\times{3.14}\times{9.1\times{10^{-31}}}\times{0.1\times{10^{-10}}}}\:}$

$\longmapsto\:\bf{\triangle{v}\:=\:\dfrac{6.626\times{10^{-34}}}{11.4296\times{10^{-41}}}\:}$

$\longmapsto\:\bf{\triangle{v}\:=\:0.5797\times{10^{7}}\:}$

$\longmapsto\:\bf\green{\triangle{v}\:=\:5.797\times{10^{6}}\:m.s^{-1}}$

$\huge\red\therefore$ The uncertainty involved in the measurement of its velocity is $\bf{\triangle{v}\:,i.e.\:\blue{5.797\times{10^{6}}\:m.s^{-1}}}$.