{"product_id":"starka-stark-effect","title":"Starka – The Stark Effect \/ Linear Splitting in Hydrogen Physics Sticker","description":"\u003cp\u003eStarka, an armoured knight, holds two charged plates apart, and a red spectral line between them splits into a fan of lines.\u003c\/p\u003e\u003ch3\u003eThe Physics\u003c\/h3\u003e\u003cp\u003ePut atoms in a strong electric field and their spectral lines split and shift. Johannes Stark observed this in hydrogen in 1913 and published it in full in Annalen der Physik (“Beobachtungen über den Effekt des elektrischen Feldes auf Spektrallinien”, Ann. Phys. 348, 965, 1914). Antonino Lo Surdo saw it independently the same year. Hydrogen is special: states with the same n but different shapes have the same energy, so the field mixes them and the shift is proportional to the field itself, giving a symmetric pattern of components.\u003c\/p\u003e\u003cp\u003e\u003cstrong\u003eΔE = (3\/2) n (n\u003csub\u003e1\u003c\/sub\u003e − n\u003csub\u003e2\u003c\/sub\u003e) e a\u003csub\u003e0\u003c\/sub\u003e F\u003c\/strong\u003e\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eΔE: energy shift of the level (J)\u003c\/li\u003e\n\u003cli\u003en: principal quantum number\u003c\/li\u003e\n\u003cli\u003en\u003csub\u003e1\u003c\/sub\u003e, n\u003csub\u003e2\u003c\/sub\u003e: parabolic quantum numbers\u003c\/li\u003e\n\u003cli\u003ee: elementary charge (C)\u003c\/li\u003e\n\u003cli\u003ea\u003csub\u003e0\u003c\/sub\u003e: Bohr radius (m)\u003c\/li\u003e\n\u003cli\u003eF: electric field strength (V\/m)\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eStark received the 1919 Nobel Prize in Physics, partly for this discovery. The linear splitting was one of the early successes of the quantum theory of the atom.\u003c\/p\u003e\u003cp\u003e\u003cem\u003eHonest caveat:\u003c\/em\u003e The linear shift is for hydrogen, to first order. Most other atoms have no such degeneracy and shift quadratically, ΔE ∝ F², and even hydrogen picks up quadratic terms in strong fields.\u003c\/p\u003e\u003ch3\u003eOn the sticker\u003c\/h3\u003e\u003cp\u003eStarka grips two round plates as a red beam between them fans out into several lines. Printed text: \u003cstrong\u003eSTARKA\u003c\/strong\u003e with the line \u003cstrong\u003eΔE ∝ F (LINEAR, H)\u003c\/strong\u003e. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.\u003c\/p\u003e","brand":"Printify","offers":[{"title":"2\" × 2\" \/ White","offer_id":50963984023655,"sku":"13526807663747358898","price":4.99,"currency_code":"USD","in_stock":true},{"title":"3\" × 3\" \/ White","offer_id":50963984056423,"sku":"65719236993534246407","price":6.99,"currency_code":"USD","in_stock":true},{"title":"4\" × 4\" \/ White","offer_id":50963984089191,"sku":"21128264090893022127","price":8.99,"currency_code":"USD","in_stock":true},{"title":"6\" × 6\" \/ White","offer_id":50963984121959,"sku":"84352653111560030142","price":11.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0596\/8746\/9159\/files\/12476091193212131114_1200.jpg?v=1793657671","url":"https:\/\/pixelatedphysics.com\/it\/products\/starka-stark-effect","provider":"Pixelated Physics","version":"1.0","type":"link"}