Physicspedia

Energy quantization is the concept that energy, particularly within atoms and molecules, can only exist in discrete, specific amounts, rather than continuously variable values. This means electrons can only occupy certain energy levels, absorbing or emitting energy in “quanta” or discrete bundles to transition between these levels.
"Energy quantization is the concept that energy, particularly within atoms and molecules, can only exist in discrete, specific amounts, rather than continuously variable values. This means electrons can only occupy certain energy levels, absorbing or emitting energy in “quanta” or discrete bundles to transition between these levels"

NOBEL PRIZE in Physics 2023

I reached my destination
and you too!'
: Chandrayaan-3

has successfully
soft-landed on the moon 🌖!.

Congratulations, India🇮🇳!

𝑰𝒏 𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄𝒔, 𝒂 𝒏𝒐𝒓𝒎𝒂𝒍 𝒅𝒊𝒔𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 𝒐𝒓 𝑮𝒂𝒖𝒔𝒔𝒊𝒂𝒏 𝒅𝒊𝒔𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 𝒊𝒔 𝒂 𝒕𝒚𝒑𝒆 𝒐𝒇 𝒄𝒐𝒏𝒕𝒊𝒏𝒖𝒐𝒖𝒔 𝒑𝒓𝒐𝒃𝒂𝒃𝒊𝒍𝒊𝒕𝒚 𝒅𝒊𝒔𝒕𝒓𝒊𝒃𝒖𝒕𝒊𝒐𝒏 𝒇𝒐𝒓 𝒂 𝒓𝒆𝒂𝒍-𝒗𝒂𝒍𝒖𝒆𝒅 𝒓𝒂𝒏𝒅𝒐𝒎 𝒗𝒂𝒓𝒊𝒂𝒃𝒍𝒆.

𝑬𝒊𝒈𝒆𝒏𝒇𝒖𝒏𝒄𝒕𝒊𝒐𝒏𝒔 𝒂𝒏𝒅 𝑬𝒊𝒈𝒆𝒏𝒗𝒂𝒍𝒖𝒆𝒔

𝑇ℎ𝑒 𝑫𝒓𝒖𝒅𝒆 𝒎𝒐𝒅𝒆𝒍 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑤𝑎𝑠 𝑝𝑟𝑜𝑝𝑜𝑠𝑒𝑑 𝑖𝑛 1900 𝑏𝑦 𝑃𝑎𝑢𝑙 𝐷𝑟𝑢𝑑𝑒 𝑡𝑜 𝑒𝑥𝑝𝑙𝑎𝑖𝑛 𝑡ℎ𝑒 𝑡𝑟𝑎𝑛𝑠𝑝𝑜𝑟𝑡 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑖𝑒𝑠 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝑖𝑛 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑠 (𝑒𝑠𝑝𝑒𝑐𝑖𝑎𝑙𝑙𝑦 𝑚𝑒𝑡𝑎𝑙𝑠). 𝐵𝑎𝑠𝑖𝑐𝑎𝑙𝑙𝑦, 𝑂ℎ𝑚'𝑠 𝑙𝑎𝑤 𝑤𝑎𝑠 𝑤𝑒𝑙𝑙 𝑒𝑠𝑡𝑎𝑏𝑙𝑖𝑠ℎ𝑒𝑑 𝑎𝑛𝑑 𝑠𝑡𝑎𝑡𝑒𝑑 𝑡ℎ𝑎𝑡 𝑡ℎ𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝐽 𝑎𝑛𝑑 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑉 𝑑𝑟𝑖𝑣𝑖𝑛𝑔 𝑡ℎ𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑎𝑟𝑒 𝑟𝑒𝑙𝑎𝑡𝑒𝑑 𝑡𝑜 𝑡ℎ𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙. 𝑇ℎ𝑒 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑖𝑠 𝑘𝑛𝑜𝑤𝑛 𝑎𝑠 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒. 𝑊ℎ𝑒𝑛 𝑤𝑒 𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟 𝑎 𝑚𝑒𝑡𝑎𝑙 𝑜𝑓 𝑢𝑛𝑖𝑡 𝑙𝑒𝑛𝑔𝑡ℎ 𝑎𝑛𝑑 𝑢𝑛𝑖𝑡 𝑐𝑟𝑜𝑠𝑠 𝑠𝑒𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝑎𝑟𝑒𝑎, 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑎𝑛𝑐𝑒 𝑖𝑠 𝑘𝑛𝑜𝑤𝑛 𝑎𝑠 𝑡ℎ𝑒 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑖𝑣𝑖𝑡𝑦, 𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 𝑡ℎ𝑒 𝑖𝑛𝑣𝑒𝑟𝑠𝑒 𝑜𝑓 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦. 𝑇ℎ𝑒 𝐷𝑟𝑢𝑑𝑒 𝑚𝑜𝑑𝑒𝑙 𝑎𝑡𝑡𝑒𝑚𝑝𝑡𝑠 𝑡𝑜 𝑒𝑥𝑝𝑙𝑎𝑖𝑛 𝑡ℎ𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦 𝑜𝑓 𝑎 𝑐𝑜𝑛𝑑𝑢𝑐𝑡𝑜𝑟 𝑖𝑛 𝑡𝑒𝑟𝑚𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑐𝑎𝑡𝑡𝑒𝑟𝑖𝑛𝑔 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 (𝑡ℎ𝑒 𝑐𝑎𝑟𝑟𝑖𝑒𝑟𝑠 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑖𝑡𝑦) 𝑏𝑦 𝑡ℎ𝑒 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒𝑙𝑦 𝑖𝑚𝑚𝑜𝑏𝑖𝑙𝑒 𝑖𝑜𝑛𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑚𝑒𝑡𝑎𝑙 𝑡ℎ𝑎𝑡 𝑎𝑐𝑡 𝑙𝑖𝑘𝑒 𝑜𝑏𝑠𝑡𝑟𝑢𝑐𝑡𝑖𝑜𝑛𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑓𝑙𝑜𝑤 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠.

𝑇ℎ𝑒 𝑚𝑒𝑡ℎ𝑜𝑑 𝑜𝑓 𝑖𝑚𝑎𝑔𝑒 𝑐ℎ𝑎𝑟𝑔𝑒𝑠 (𝑎𝑙𝑠𝑜 𝑘𝑛𝑜𝑤𝑛 𝑎𝑠 𝑡ℎ𝑒 𝑚𝑒𝑡ℎ𝑜𝑑 𝑜𝑓 𝑖𝑚𝑎𝑔𝑒𝑠 𝑎𝑛𝑑 𝑚𝑒𝑡ℎ𝑜𝑑 𝑜𝑓 𝑚𝑖𝑟𝑟𝑜𝑟 𝑐ℎ𝑎𝑟𝑔𝑒𝑠) 𝑖𝑠 𝑎 𝑏𝑎𝑠𝑖𝑐 𝑝𝑟𝑜𝑏𝑙𝑒𝑚-𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑡𝑜𝑜𝑙 𝑖𝑛 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑠𝑡𝑎𝑡𝑖𝑐𝑠. 𝑇ℎ𝑒 𝑛𝑎𝑚𝑒 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑡𝑒𝑠 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑟𝑒𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 𝑜𝑓 𝑐𝑒𝑟𝑡𝑎𝑖𝑛 𝑒𝑙𝑒𝑚𝑒𝑛𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑜𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑙𝑎𝑦𝑜𝑢𝑡 𝑤𝑖𝑡ℎ 𝑖𝑚𝑎𝑔𝑖𝑛𝑎𝑟𝑦 𝑐ℎ𝑎𝑟𝑔𝑒𝑠, 𝑤ℎ𝑖𝑐ℎ 𝑟𝑒𝑝𝑙𝑖𝑐𝑎𝑡𝑒𝑠 𝑡ℎ𝑒 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑟𝑜𝑏𝑙𝑒𝑚 (𝑠𝑒𝑒 𝐷𝑖𝑟𝑖𝑐ℎ𝑙𝑒𝑡 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠 𝑜𝑟 𝑁𝑒𝑢𝑚𝑎𝑛𝑛 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛𝑠).

𝑇𝑖𝑚𝑒 𝑑𝑖𝑙𝑎𝑡𝑖𝑜𝑛 𝑖𝑠 𝑡ℎ𝑒 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑒𝑙𝑎𝑝𝑠𝑒𝑑 𝑡𝑖𝑚𝑒 𝑎𝑠 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑏𝑦 𝑡𝑤𝑜 𝑐𝑙𝑜𝑐𝑘𝑠, 𝑒𝑖𝑡ℎ𝑒𝑟 𝑑𝑢𝑒 𝑡𝑜 𝑎 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡ℎ𝑒𝑚 (𝑠𝑝𝑒𝑐𝑖𝑎𝑙 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑖𝑡𝑦) 𝑜𝑟 𝑑𝑢𝑒 𝑡𝑜 𝑎 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡ℎ𝑒𝑖𝑟 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛𝑠 (𝑔𝑒𝑛𝑒𝑟𝑎𝑙 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑖𝑡𝑦). 𝑊ℎ𝑒𝑛 𝑢𝑛𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑑, "𝑡𝑖𝑚𝑒 𝑑𝑖𝑙𝑎𝑡𝑖𝑜𝑛" 𝑢𝑠𝑢𝑎𝑙𝑙𝑦 𝑟𝑒𝑓𝑒𝑟𝑠 𝑡𝑜 𝑡ℎ𝑒 𝑒𝑓𝑓𝑒𝑐𝑡 𝑑𝑢𝑒 𝑡𝑜 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦.
𝐴𝑓𝑡𝑒𝑟 𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑖𝑛𝑔 𝑓𝑜𝑟 𝑣𝑎𝑟𝑦𝑖𝑛𝑔 𝑠𝑖𝑔𝑛𝑎𝑙 𝑑𝑒𝑙𝑎𝑦𝑠 𝑑𝑢𝑒 𝑡𝑜 𝑡ℎ𝑒 𝑐ℎ𝑎𝑛𝑔𝑖𝑛𝑔 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑎𝑛 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟 𝑎𝑛𝑑 𝑎 𝑚𝑜𝑣𝑖𝑛𝑔 𝑐𝑙𝑜𝑐𝑘 (𝑖.𝑒. 𝐷𝑜𝑝𝑝𝑙𝑒𝑟 𝑒𝑓𝑓𝑒𝑐𝑡), 𝑡ℎ𝑒 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟 𝑤𝑖𝑙𝑙 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑡ℎ𝑒 𝑚𝑜𝑣𝑖𝑛𝑔 𝑐𝑙𝑜𝑐𝑘 𝑎𝑠 𝑡𝑖𝑐𝑘𝑖𝑛𝑔 𝑠𝑙𝑜𝑤𝑒𝑟 𝑡ℎ𝑎𝑛 𝑎 𝑐𝑙𝑜𝑐𝑘 𝑡ℎ𝑎𝑡 𝑖𝑠 𝑎𝑡 𝑟𝑒𝑠𝑡 𝑖𝑛 𝑡ℎ𝑒 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑟'𝑠 𝑜𝑤𝑛 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑓𝑟𝑎𝑚𝑒. 𝐼𝑛 𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛, 𝑎 𝑐𝑙𝑜𝑐𝑘 𝑡ℎ𝑎𝑡 𝑖𝑠 𝑐𝑙𝑜𝑠𝑒 𝑡𝑜 𝑎 𝑚𝑎𝑠𝑠𝑖𝑣𝑒 𝑏𝑜𝑑𝑦 𝑤𝑖𝑙𝑙 𝑟𝑒𝑐𝑜𝑟𝑑 𝑙𝑒𝑠𝑠 𝑒𝑙𝑎𝑝𝑠𝑒𝑑 𝑡𝑖𝑚𝑒 𝑡ℎ𝑎𝑛 𝑎 𝑐𝑙𝑜𝑐𝑘 𝑠𝑖𝑡𝑢𝑎𝑡𝑒𝑑 𝑓𝑢𝑟𝑡ℎ𝑒𝑟 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑠𝑎𝑖𝑑 𝑚𝑎𝑠𝑠𝑖𝑣𝑒 𝑏𝑜𝑑𝑦 (𝑎𝑛𝑑 𝑤ℎ𝑖𝑐ℎ 𝑖𝑠 𝑎𝑡 𝑎 ℎ𝑖𝑔ℎ𝑒𝑟 𝑔𝑟𝑎𝑣𝑖𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙).
𝑇ℎ𝑒𝑠𝑒 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑜𝑛𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑒𝑜𝑟𝑦 𝑜𝑓 𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑖𝑡𝑦 ℎ𝑎𝑣𝑒 𝑏𝑒𝑒𝑛 𝑟𝑒𝑝𝑒𝑎𝑡𝑒𝑑𝑙𝑦 𝑐𝑜𝑛𝑓𝑖𝑟𝑚𝑒𝑑 𝑏𝑦 𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡, 𝑎𝑛𝑑 𝑡ℎ𝑒𝑦 𝑎𝑟𝑒 𝑜𝑓 𝑝𝑟𝑎𝑐𝑡𝑖𝑐𝑎𝑙 𝑐𝑜𝑛𝑐𝑒𝑟𝑛, 𝑓𝑜𝑟 𝑖𝑛𝑠𝑡𝑎𝑛𝑐𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑎𝑡𝑒𝑙𝑙𝑖𝑡𝑒 𝑛𝑎𝑣𝑖𝑔𝑎𝑡𝑖𝑜𝑛 𝑠𝑦𝑠𝑡𝑒𝑚𝑠 𝑠𝑢𝑐ℎ 𝑎𝑠 𝐺𝑃𝑆 𝑎𝑛𝑑 𝐺𝑎𝑙𝑖𝑙𝑒𝑜.

𝐹𝑖𝑛𝑑𝑖𝑛𝑔 𝑡ℎ𝑒 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑓𝑖𝑒𝑙𝑑 𝑖𝑛𝑠𝑖𝑑𝑒 𝑎 𝑡𝑜𝑟𝑜𝑖𝑑 𝑖𝑠 𝑎 𝑔𝑜𝑜𝑑 𝑒𝑥𝑎𝑚𝑝𝑙𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑜𝑤𝑒𝑟 𝑜𝑓 𝐴𝑚𝑝𝑒𝑟𝑒'𝑠 𝑙𝑎𝑤. 𝑇ℎ𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑒𝑛𝑐𝑙𝑜𝑠𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑑𝑎𝑠ℎ𝑒𝑑 𝑙𝑖𝑛𝑒 𝑖𝑠 𝑗𝑢𝑠𝑡 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑙𝑜𝑜𝑝𝑠 𝑡𝑖𝑚𝑒𝑠 𝑡ℎ𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑖𝑛 𝑒𝑎𝑐ℎ 𝑙𝑜𝑜𝑝. 𝐴𝑚𝑝𝑒𝑟𝑒𝑠 𝑙𝑎𝑤 𝑡ℎ𝑒𝑛 𝑔𝑖𝑣𝑒𝑠 𝑡ℎ𝑒 𝑚𝑎𝑔𝑛𝑒𝑡𝑖𝑐 𝑓𝑖𝑒𝑙𝑑 𝑏𝑦
𝐵=(𝜇𝑁𝐼)/2𝜋𝑟
𝑇ℎ𝑒 𝑡𝑜𝑟𝑜𝑖𝑑 𝑖𝑠 𝑎 𝑢𝑠𝑒𝑓𝑢𝑙 𝑑𝑒𝑣𝑖𝑐𝑒 𝑢𝑠𝑒𝑑 𝑖𝑛 𝑒𝑣𝑒𝑟𝑦𝑡ℎ𝑖𝑛𝑔 𝑓𝑟𝑜𝑚 𝑡𝑎𝑝𝑒 ℎ𝑒𝑎𝑑𝑠 𝑡𝑜 𝑡𝑜𝑘𝑎𝑚𝑎𝑘𝑠.

𝑀𝑎𝑡𝑡𝑒𝑟 𝑤𝑎𝑣𝑒𝑠 𝑎𝑟𝑒 𝑎 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑝𝑎𝑟𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑡ℎ𝑒𝑜𝑟𝑦 𝑜𝑓 𝑞𝑢𝑎𝑛𝑡𝑢𝑚 𝑚𝑒𝑐ℎ𝑎𝑛𝑖𝑐𝑠, 𝑏𝑒𝑖𝑛𝑔 ℎ𝑎𝑙𝑓 𝑜𝑓 𝑤𝑎𝑣𝑒–𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑑𝑢𝑎𝑙𝑖𝑡𝑦. 𝐴𝑙𝑙 𝑚𝑎𝑡𝑡𝑒𝑟 𝑒𝑥ℎ𝑖𝑏𝑖𝑡𝑠 𝑤𝑎𝑣𝑒-𝑙𝑖𝑘𝑒 𝑏𝑒ℎ𝑎𝑣𝑖𝑜𝑟. 𝐹𝑜𝑟 𝑒𝑥𝑎𝑚𝑝𝑙𝑒, 𝑎 𝑏𝑒𝑎𝑚 𝑜𝑓 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝑐𝑎𝑛 𝑏𝑒 𝑑𝑖𝑓𝑓𝑟𝑎𝑐𝑡𝑒𝑑 𝑗𝑢𝑠𝑡 𝑙𝑖𝑘𝑒 𝑎 𝑏𝑒𝑎𝑚 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡 𝑜𝑟 𝑎 𝑤𝑎𝑡𝑒𝑟 𝑤𝑎𝑣𝑒.
𝑇ℎ𝑒 𝑐𝑜𝑛𝑐𝑒𝑝𝑡 𝑡ℎ𝑎𝑡 𝑚𝑎𝑡𝑡𝑒𝑟 𝑏𝑒ℎ𝑎𝑣𝑒𝑠 𝑙𝑖𝑘𝑒 𝑎 𝑤𝑎𝑣𝑒 𝑤𝑎𝑠 𝑝𝑟𝑜𝑝𝑜𝑠𝑒𝑑 𝑏𝑦 𝐹𝑟𝑒𝑛𝑐ℎ 𝑝ℎ𝑦𝑠𝑖𝑐𝑖𝑠𝑡 𝐿𝑜𝑢𝑖𝑠 𝑑𝑒 𝐵𝑟𝑜𝑔𝑙𝑖𝑒 𝑖𝑛 1924, 𝑎𝑛𝑑 𝑠𝑜 𝑚𝑎𝑡𝑡𝑒𝑟 𝑤𝑎𝑣𝑒𝑠 𝑎𝑟𝑒 𝑎𝑙𝑠𝑜 𝑘𝑛𝑜𝑤𝑛 𝑎𝑠 𝑑𝑒 𝐵𝑟𝑜𝑔𝑙𝑖𝑒 𝑤𝑎𝑣𝑒𝑠.
𝑇ℎ𝑒 𝑑𝑒 𝐵𝑟𝑜𝑔𝑙𝑖𝑒 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ 𝑖𝑠 𝑡ℎ𝑒 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ, 𝜆, 𝑎𝑠𝑠𝑜𝑐𝑖𝑎𝑡𝑒𝑑 𝑤𝑖𝑡ℎ 𝑎 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒 𝑤𝑖𝑡ℎ 𝑚𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝑝 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑡ℎ𝑒 𝑃𝑙𝑎𝑛𝑐𝑘 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, ℎ:
ℎ=𝑝/𝜆