Question

debroglie wavelength of thermal neutron at t degree kelvin is:

Answer 1

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⬆️⬆️⬆️⬆️⬆️⛔⛔⛔♦️♦️♦️A nuclear reactor emits thermal neutrons. ... Kelvin temperature T. We learned in Section 14-3 that the average kinetic energy of a ... Calculate the de Broglie wavelength of an average.

Answer 2

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ɪɴ ᴘʜʏsɪᴄs, ᴛʜᴇ ᴛʜᴇʀᴍᴀʟ ᴅᴇ ʙʀᴏɢʟɪᴇ ᴡᴀᴠᴇʟᴇɴɢᴛʜ({\ᴅɪsᴘʟᴀʏsᴛʏʟᴇ \ʟᴀᴍʙᴅᴀ _{\ᴍᴀᴛʜʀᴍ {ᴛʜ} }}) ɪs ʀᴏᴜɢʜʟʏ ᴛʜᴇ ᴀᴠᴇʀᴀɢᴇ ᴅᴇ ʙʀᴏɢʟɪᴇ ᴡᴀᴠᴇʟᴇɴɢᴛʜ ᴏғ ᴛʜᴇ ɢᴀs ᴘᴀʀᴛɪᴄʟᴇs ɪɴ ᴀɴ ɪᴅᴇᴀʟ ɢᴀs ᴀᴛ ᴛʜᴇ sᴘᴇᴄɪғɪᴇᴅ ᴛᴇᴍᴘᴇʀᴀᴛᴜʀᴇ. ᴡᴇ ᴄᴀɴ ᴛᴀᴋᴇ ᴛʜᴇ ᴀᴠᴇʀᴀɢᴇ ɪɴᴛᴇʀᴘᴀʀᴛɪᴄʟᴇ sᴘᴀᴄɪɴɢ ɪɴ ᴛʜᴇ ɢᴀs ᴛᴏ ʙᴇ ᴀᴘᴘʀᴏxɪᴍᴀᴛᴇʟʏ (ᴠ/ɴ)1/3 ᴡʜᴇʀᴇ ᴠ ɪs ᴛʜᴇ ᴠᴏʟᴜᴍᴇ ᴀɴᴅ ɴ ɪs ᴛʜᴇ ɴᴜᴍʙᴇʀ ᴏғ ᴘᴀʀᴛɪᴄʟᴇs. ᴡʜᴇɴ ᴛʜᴇ ᴛʜᴇʀᴍᴀʟ ᴅᴇ ʙʀᴏɢʟɪᴇ ᴡᴀᴠᴇʟᴇɴɢᴛʜ ɪs ᴍᴜᴄʜ sᴍᴀʟʟᴇʀ ᴛʜᴀɴ ᴛʜᴇ ɪɴᴛᴇʀᴘᴀʀᴛɪᴄʟᴇ ᴅɪsᴛᴀɴᴄᴇ, ᴛʜᴇ ɢᴀs ᴄᴀɴ ʙᴇ ᴄᴏɴsɪᴅᴇʀᴇᴅ ᴛᴏ ʙᴇ ᴀ ᴄʟᴀssɪᴄᴀʟ ᴏʀ ᴍᴀxᴡᴇʟʟ–ʙᴏʟᴛᴢᴍᴀɴɴ ɢᴀs. ᴏɴ ᴛʜᴇ ᴏᴛʜᴇʀ ʜᴀɴᴅ, ᴡʜᴇɴ ᴛʜᴇ ᴛʜᴇʀᴍᴀʟ ᴅᴇ ʙʀᴏɢʟɪᴇ ᴡᴀᴠᴇʟᴇɴɢᴛʜ ɪs ᴏɴ ᴛʜᴇ ᴏʀᴅᴇʀ ᴏғ ᴏʀ ʟᴀʀɢᴇʀ ᴛʜᴀɴ ᴛʜᴇ ɪɴᴛᴇʀᴘᴀʀᴛɪᴄʟᴇ ᴅɪsᴛᴀɴᴄᴇ, ǫᴜᴀɴᴛᴜᴍ ᴇғғᴇᴄᴛs ᴡɪʟʟ ᴅᴏᴍɪɴᴀᴛᴇ ᴀɴᴅ ᴛʜᴇ ɢᴀs ᴍᴜsᴛ ʙᴇ ᴛʀᴇᴀᴛᴇᴅ ᴀs ᴀ ғᴇʀᴍɪ ɢᴀs ᴏʀ ᴀ ʙᴏsᴇ ɢᴀs, ᴅᴇᴘᴇɴᴅɪɴɢ ᴏɴ ᴛʜᴇ ɴᴀᴛᴜʀᴇ ᴏғ ᴛʜᴇ ɢᴀs ᴘᴀʀᴛɪᴄʟᴇs. ᴛʜᴇ ᴄʀɪᴛɪᴄᴀʟ ᴛᴇᴍᴘᴇʀᴀᴛᴜʀᴇ ɪs ᴛʜᴇ ᴛʀᴀɴsɪᴛɪᴏɴ ᴘᴏɪɴᴛ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇsᴇ ᴛᴡᴏ ʀᴇɢɪᴍᴇs, ᴀɴᴅ ᴀᴛ ᴛʜɪs ᴄʀɪᴛɪᴄᴀʟ ᴛᴇᴍᴘᴇʀᴀᴛᴜʀᴇ, ᴛʜᴇ ᴛʜᴇʀᴍᴀʟ ᴡᴀᴠᴇʟᴇɴɢᴛʜ ᴡɪʟʟ ʙᴇ ᴀᴘᴘʀᴏxɪᴍᴀᴛᴇʟʏ ᴇǫᴜᴀʟ ᴛᴏ ᴛʜᴇ ɪɴᴛᴇʀᴘᴀʀᴛɪᴄʟᴇ ᴅɪsᴛᴀɴᴄᴇ. ᴛʜᴀᴛ ɪs, ᴛʜᴇ ǫᴜᴀɴᴛᴜᴍ ɴᴀᴛᴜʀᴇ ᴏғ ᴛʜᴇ ɢᴀs ᴡɪʟʟ ʙᴇ ᴇᴠɪᴅᴇɴᴛ ғᴏʀ

{\ᴅɪsᴘʟᴀʏsᴛʏʟᴇ \ᴅɪsᴘʟᴀʏsᴛʏʟᴇ {\ғʀᴀᴄ {ᴠ}{ɴ\ʟᴀᴍʙᴅᴀ _{\ᴍᴀᴛʜʀᴍ {ᴛʜ} }^{3}}}\ʟᴇǫ 1\ ,{\ʀᴍ {ᴏʀ}}\ \ʟᴇғᴛ({\ғʀᴀᴄ {ᴠ}{ɴ}}\ʀɪɢʜᴛ)^{1/3}\ʟᴇǫ \ʟᴀᴍʙᴅᴀ _{\ᴍᴀᴛʜʀᴍ {ᴛʜ} }}

ɪ.ᴇ., ᴡʜᴇɴ ᴛʜᴇ ɪɴᴛᴇʀᴘᴀʀᴛɪᴄʟᴇ ᴅɪsᴛᴀɴᴄᴇ ɪs ʟᴇss ᴛʜᴀɴ ᴛʜᴇ ᴛʜᴇʀᴍᴀʟ ᴅᴇ ʙʀᴏɢʟɪᴇ ᴡᴀᴠᴇʟᴇɴɢᴛʜ; ɪɴ ᴛʜɪs ᴄᴀsᴇ ᴛʜᴇ ɢᴀs ᴡɪʟʟ ᴏʙᴇʏ ʙᴏsᴇ–ᴇɪɴsᴛᴇɪɴ sᴛᴀᴛɪsᴛɪᴄs ᴏʀ ғᴇʀᴍɪ–ᴅɪʀᴀᴄ sᴛᴀᴛɪsᴛɪᴄs, ᴡʜɪᴄʜᴇᴠᴇʀ ɪs ᴀᴘᴘʀᴏᴘʀɪᴀᴛᴇ. ᴛʜɪs ɪs ғᴏʀ ᴇxᴀᴍᴘʟᴇ ᴛʜᴇ ᴄᴀsᴇ ғᴏʀ ᴇʟᴇᴄᴛʀᴏɴs ɪɴ ᴀ ᴛʏᴘɪᴄᴀʟ ᴍᴇᴛᴀʟ ᴀᴛ ᴛ = 300 ᴋ, ᴡʜᴇʀᴇ ᴛʜᴇ ᴇʟᴇᴄᴛʀᴏɴ ɢᴀs ᴏʙᴇʏs ғᴇʀᴍɪ–ᴅɪʀᴀᴄ sᴛᴀᴛɪsᴛɪᴄs, ᴏʀ ɪɴ ᴀ ʙᴏsᴇ–ᴇɪɴsᴛᴇɪɴ ᴄᴏɴᴅᴇɴsᴀᴛᴇ. ᴏɴ ᴛʜᴇ ᴏᴛʜᴇʀ ʜᴀɴᴅ, ғᴏʀ

{\ᴅɪsᴘʟᴀʏsᴛʏʟᴇ \ᴅɪsᴘʟᴀʏsᴛʏʟᴇ {\ғʀᴀᴄ {ᴠ}{ɴ\ʟᴀᴍʙᴅᴀ _{\ᴍᴀᴛʜʀᴍ {ᴛʜ} }^{3}}}\ɢɢ 1\ ,{\ʀᴍ {ᴏʀ}}\ \ʟᴇғᴛ({\ғʀᴀᴄ {ᴠ}{ɴ}}\ʀɪɢʜᴛ)^{1/3}\ɢɢ \ʟᴀᴍʙᴅᴀ _{\ᴍᴀᴛʜʀᴍ {ᴛʜ} }}

ɪ.ᴇ., ᴡʜᴇɴ ᴛʜᴇ ɪɴᴛᴇʀᴘᴀʀᴛɪᴄʟᴇ ᴅɪsᴛᴀɴᴄᴇ ɪs ᴍᴜᴄʜ ʟᴀʀɢᴇʀ ᴛʜᴀɴ ᴛʜᴇ ᴛʜᴇʀᴍᴀʟ ᴅᴇ ʙʀᴏɢʟɪᴇ ᴡᴀᴠᴇʟᴇɴɢᴛʜ, ᴛʜᴇ ɢᴀs ᴡɪʟʟ ᴏʙᴇʏ ᴍᴀxᴡᴇʟʟ–ʙᴏʟᴛᴢᴍᴀɴɴ sᴛᴀᴛɪsᴛɪᴄs.[1] sᴜᴄʜ ɪs ᴛʜᴇ ᴄᴀsᴇ ғᴏʀ ᴍᴏʟᴇᴄᴜʟᴀʀ ᴏʀ ᴀᴛᴏᴍɪᴄ ɢᴀsᴇs ᴀᴛ ʀᴏᴏᴍ ᴛᴇᴍᴘᴇʀᴀᴛᴜʀᴇ, ᴀɴᴅ ғᴏʀ ᴛʜᴇʀᴍᴀʟ ɴᴇᴜᴛʀᴏɴs ᴘʀᴏᴅᴜᴄᴇᴅ ʙʏ ᴀ ɴᴇᴜᴛʀᴏɴ sᴏᴜʀᴄᴇ.