Why deviation of alpha particle is less than beta particle?
Answers
Answered by
1
☺ HIII FRD HERE UR ANS ☺
..
⬆️ I HOPE HELP
....
⬆️⬆️⬆️⬆️⬆️⛔⛔⛔♦️♦️♦️
The animation below shows the deflection of radiation in an electric field. ... Beta particles are attracted to the positively charged plate.
..
⬆️ I HOPE HELP
....
⬆️⬆️⬆️⬆️⬆️⛔⛔⛔♦️♦️♦️
The animation below shows the deflection of radiation in an electric field. ... Beta particles are attracted to the positively charged plate.
Answered by
12
ᴛʜᴇ ғᴏʀᴄᴇ ᴏɴ ᴄʜᴀʀɢᴇ ǫ ᴍᴏᴠɪɴɢ ɪɴ ᴍᴀɢɴᴇᴛɪᴄ ғɪᴇʟᴅ ᴡɪᴛʜ ᴠᴇʟᴏᴄɪᴛʏ ᴠ ɪs ǫ(ᴠxʙ). ᴛʜɪs ғᴏʀᴄᴇ ɪs ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ᴛᴏ ᴠ ᴀɴᴅ ʜᴇɴᴄᴇ ᴀᴄᴛs ᴀs ᴄᴇɴᴛʀɪᴘᴇᴛᴀʟ ғᴏʀᴄᴇ ᴍᴠ^2/ʀ. ғᴏʀ sɪᴍᴘʟɪᴄɪᴛʏ ɪғ ᴡᴇ ᴛᴀᴋᴇ ᴠᴇʟᴏᴄɪᴛʏ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ᴛᴏ ʙ ᴛʜᴇɴ ᴠxʙ=ᴠʙ.
ɴᴏᴡ, ᴍᴠ^2/ʀ =ǫᴠʙ. ᴛʜᴇʀᴇғᴏʀᴇ ,
ʀ=ǫʙ/ᴍᴠ…………………..(1)
ᴛʜɪs ᴇǫᴜᴀᴛɪᴏɴ sʜᴏᴡs ᴛʜᴀᴛ ɪғ ᴇʟᴇᴄᴛʀᴏɴ ᴀɴᴅ (ᴀʟᴘʜᴀ) ᴘᴀʀᴛɪᴄʟᴇ ᴍᴏᴠᴇ ɪɴ ᴀ ɢɪᴠᴇɴ ᴍᴀɢɴᴇᴛɪᴄ ғɪᴇʟᴅ ʙ ᴛʜᴇɴ ʀᴀᴅɪᴜs(ᴏғ ᴄᴜʀᴠᴀᴛᴜʀᴇ ) ᴏғ ᴛʜᴇ ᴘᴀᴛʜ ᴡɪʟʟ ʙᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ (ǫ/ᴍ).
ғᴏʀ ᴇʟᴇᴄᴛʀᴏɴ (ǫ/ᴍ)=[(1.6x10^-19ᴄ)/(9.1x10^-31 ᴋɢ)]~10^12ᴄ/ᴋɢ………….(2)
ғᴏʀ ( ᴀʟᴘʜᴀ )ᴘᴀʀᴛɪᴄʟᴇ (ǫ/ᴍ)=[(3.2x10^-19ᴄ)/(4x1.66x10^-27 ᴋɢ)]~10^8…….(3)
ᴛʜᴇsᴇ ᴠᴀʟᴜᴇs sʜᴏᴡs ᴛʜᴀᴛ ᴇʟᴇᴄᴛʀᴏɴs ᴀʀᴇ ᴅᴇғʟᴇᴄᴛᴇᴅ ᴍᴏʀᴇ ᴄᴏᴍᴘᴀʀᴇᴅ ᴛᴏ (ᴀʟᴘʜᴀ) ᴘᴀʀᴛɪᴄʟᴇs ɪɴ ᴀ ɢɪᴠᴇɴ ᴍᴀɢɴᴇᴛɪᴄ ғɪᴇʟᴅ ɪғ ᴛʜᴇ ᴛʀᴀᴠᴇʟ ᴡɪᴛʜ sᴀᴍᴇ ᴠᴇʟᴏᴄɪᴛʏ.
ɴᴏᴡ, ᴄᴏɴsɪᴅᴇʀ ᴛʜᴇɪʀ ᴍᴏᴛɪᴏɴ ɪɴ ᴀ ɢɪᴠᴇɴ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ᴇ.
ᴛʜᴇ ᴇʟᴇᴄᴛʀɪᴄ ғᴏʀᴄᴇ ᴏɴ ᴇʟᴇᴄᴛʀᴏɴ ɪs ᴇᴇ. ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴀ=(ᴇᴇ/ᴍ). ᴛʜᴇ ᴅᴇғʟᴇᴄᴛɪᴏɴ ɪɴ ᴛʜᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴏғ ᴇ ɪɴ ᴛɪᴍᴇ ᴛ ɪs ʏ1=(1/2)(ᴇᴇ/ᴍ)ᴛ^2……(4)
ғᴏʀ (ᴀʟᴘʜᴀ) ᴘᴀʀᴛɪᴄʟᴇs ʏ2=(1/2)[(2ᴇᴇ/( ᴍ ᴏғ ᴀʟᴘʜᴀ)]……………..(5)
ɴᴏᴡ, ᴍ ᴏғ ᴀʟᴘʜᴀ ɪs ᴀʙᴏᴜᴛ 10^4 ᴛɪᴍᴇs ᴍ ᴏғ ᴇʟᴇᴄᴛʀᴏɴ. ʜᴇɴᴄᴇ ,ʏ1>ʏ2. ᴛʜᴇ ᴅᴇғʟᴇᴄᴛɪᴏɴ ɪs ᴍᴏʀᴇ ғᴏʀ ᴇʟᴇᴄᴛʀᴏɴs ᴄᴏᴍᴘᴀʀᴇᴅ ᴛᴏ ᴛʜᴀᴛ ᴏғ (ᴀʟᴘʜᴀ) ᴘᴀʀᴛɪᴄʟᴇs .
ʀᴇᴍᴇᴍʙᴇʀ ᴛʜᴀᴛ (ʙᴇᴛᴀ) ᴘᴀʀᴛɪᴄʟᴇs ᴀʀᴇ ᴇʟᴇᴄᴛʀᴏɴs.
ɪɴ ᴛʜᴇ ᴀʙᴏᴠᴇ ᴡᴇ ʜᴀᴠᴇ ᴀssᴜᴍᴇᴅ ᴛʜᴀᴛ (ᴀʟᴘʜᴀ) ᴀɴᴅ(ʙᴇᴛᴀ) ᴘᴀʀᴛɪᴄʟᴇs ᴇɴᴛᴇʀ ᴛʜᴇ ғɪᴇʟᴅ ᴇ ɪɴ ᴛʜᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ᴛᴏ ғɪᴇʟᴅ ᴇ. ᴀʟsᴏ, ɴᴏᴛᴇ ᴛʜᴀᴛ ᴡᴇ ʜᴀᴠᴇ ᴄᴏɴsɪᴅᴇʀᴇᴅ ᴅᴇғʟᴇᴄᴛɪᴏɴs ɪɴ sᴀᴍᴇ ᴛɪᴍᴇ ɪɴᴛᴇʀᴠᴀʟ ᴛ.
ɴᴏᴡ, ᴍᴠ^2/ʀ =ǫᴠʙ. ᴛʜᴇʀᴇғᴏʀᴇ ,
ʀ=ǫʙ/ᴍᴠ…………………..(1)
ᴛʜɪs ᴇǫᴜᴀᴛɪᴏɴ sʜᴏᴡs ᴛʜᴀᴛ ɪғ ᴇʟᴇᴄᴛʀᴏɴ ᴀɴᴅ (ᴀʟᴘʜᴀ) ᴘᴀʀᴛɪᴄʟᴇ ᴍᴏᴠᴇ ɪɴ ᴀ ɢɪᴠᴇɴ ᴍᴀɢɴᴇᴛɪᴄ ғɪᴇʟᴅ ʙ ᴛʜᴇɴ ʀᴀᴅɪᴜs(ᴏғ ᴄᴜʀᴠᴀᴛᴜʀᴇ ) ᴏғ ᴛʜᴇ ᴘᴀᴛʜ ᴡɪʟʟ ʙᴇ ᴘʀᴏᴘᴏʀᴛɪᴏɴᴀʟ ᴛᴏ (ǫ/ᴍ).
ғᴏʀ ᴇʟᴇᴄᴛʀᴏɴ (ǫ/ᴍ)=[(1.6x10^-19ᴄ)/(9.1x10^-31 ᴋɢ)]~10^12ᴄ/ᴋɢ………….(2)
ғᴏʀ ( ᴀʟᴘʜᴀ )ᴘᴀʀᴛɪᴄʟᴇ (ǫ/ᴍ)=[(3.2x10^-19ᴄ)/(4x1.66x10^-27 ᴋɢ)]~10^8…….(3)
ᴛʜᴇsᴇ ᴠᴀʟᴜᴇs sʜᴏᴡs ᴛʜᴀᴛ ᴇʟᴇᴄᴛʀᴏɴs ᴀʀᴇ ᴅᴇғʟᴇᴄᴛᴇᴅ ᴍᴏʀᴇ ᴄᴏᴍᴘᴀʀᴇᴅ ᴛᴏ (ᴀʟᴘʜᴀ) ᴘᴀʀᴛɪᴄʟᴇs ɪɴ ᴀ ɢɪᴠᴇɴ ᴍᴀɢɴᴇᴛɪᴄ ғɪᴇʟᴅ ɪғ ᴛʜᴇ ᴛʀᴀᴠᴇʟ ᴡɪᴛʜ sᴀᴍᴇ ᴠᴇʟᴏᴄɪᴛʏ.
ɴᴏᴡ, ᴄᴏɴsɪᴅᴇʀ ᴛʜᴇɪʀ ᴍᴏᴛɪᴏɴ ɪɴ ᴀ ɢɪᴠᴇɴ ᴇʟᴇᴄᴛʀɪᴄ ғɪᴇʟᴅ ᴇ.
ᴛʜᴇ ᴇʟᴇᴄᴛʀɪᴄ ғᴏʀᴄᴇ ᴏɴ ᴇʟᴇᴄᴛʀᴏɴ ɪs ᴇᴇ. ᴛʜᴇ ᴀᴄᴄᴇʟᴇʀᴀᴛɪᴏɴ ᴀ=(ᴇᴇ/ᴍ). ᴛʜᴇ ᴅᴇғʟᴇᴄᴛɪᴏɴ ɪɴ ᴛʜᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴏғ ᴇ ɪɴ ᴛɪᴍᴇ ᴛ ɪs ʏ1=(1/2)(ᴇᴇ/ᴍ)ᴛ^2……(4)
ғᴏʀ (ᴀʟᴘʜᴀ) ᴘᴀʀᴛɪᴄʟᴇs ʏ2=(1/2)[(2ᴇᴇ/( ᴍ ᴏғ ᴀʟᴘʜᴀ)]……………..(5)
ɴᴏᴡ, ᴍ ᴏғ ᴀʟᴘʜᴀ ɪs ᴀʙᴏᴜᴛ 10^4 ᴛɪᴍᴇs ᴍ ᴏғ ᴇʟᴇᴄᴛʀᴏɴ. ʜᴇɴᴄᴇ ,ʏ1>ʏ2. ᴛʜᴇ ᴅᴇғʟᴇᴄᴛɪᴏɴ ɪs ᴍᴏʀᴇ ғᴏʀ ᴇʟᴇᴄᴛʀᴏɴs ᴄᴏᴍᴘᴀʀᴇᴅ ᴛᴏ ᴛʜᴀᴛ ᴏғ (ᴀʟᴘʜᴀ) ᴘᴀʀᴛɪᴄʟᴇs .
ʀᴇᴍᴇᴍʙᴇʀ ᴛʜᴀᴛ (ʙᴇᴛᴀ) ᴘᴀʀᴛɪᴄʟᴇs ᴀʀᴇ ᴇʟᴇᴄᴛʀᴏɴs.
ɪɴ ᴛʜᴇ ᴀʙᴏᴠᴇ ᴡᴇ ʜᴀᴠᴇ ᴀssᴜᴍᴇᴅ ᴛʜᴀᴛ (ᴀʟᴘʜᴀ) ᴀɴᴅ(ʙᴇᴛᴀ) ᴘᴀʀᴛɪᴄʟᴇs ᴇɴᴛᴇʀ ᴛʜᴇ ғɪᴇʟᴅ ᴇ ɪɴ ᴛʜᴇ ᴅɪʀᴇᴄᴛɪᴏɴ ᴘᴇʀᴘᴇɴᴅɪᴄᴜʟᴀʀ ᴛᴏ ғɪᴇʟᴅ ᴇ. ᴀʟsᴏ, ɴᴏᴛᴇ ᴛʜᴀᴛ ᴡᴇ ʜᴀᴠᴇ ᴄᴏɴsɪᴅᴇʀᴇᴅ ᴅᴇғʟᴇᴄᴛɪᴏɴs ɪɴ sᴀᴍᴇ ᴛɪᴍᴇ ɪɴᴛᴇʀᴠᴀʟ ᴛ.
Similar questions