किसी भी मात्रा को या चीज़ को जिस भी शब्द से बताया जाता है उसे उसका मात्रक कहते हैं, जैसे लंबाई का मात्रक मीटर है !
मात्रक (Unit)
मात्रक दो प्रकार के होते हैं (1) मूल मात्रक तथा (2) व्युत्पन्न मात्रक
मूल भौतिक राशियों, यानि मुख्य चीजों, जैसे लम्बाई. द्रव्यमान, समय, आदि के मात्रकों को ‘मूल मात्रक’ (Basic units) कहते हैं तथा व्युत्पन्न राशियों (जो मुख्य राशियों से बनी हैं) (मूल राशियों के अतिरिक्त सभी राशियां) के मात्रकों को ‘व्युत्पन्न मात्रक‘ (Derived units) कहते हैं। उदाहरण के लिए द्रव्यमान (Mass), लम्बाई व समय के मात्रक क्रमश: किलोग्राम, मीटर व सेकण्ड हैं !
मात्रक कैसे निर्धारित हुए ?
मूल मात्रक 1971 में माप और तौल की अन्तर्राष्ट्रीय समिति द्वारा पदार्थ की मात्रा की मूल राशि मानते हुए मोल को इसका मूल मात्रक निर्धारित किया गया। इस प्रकार सात भौतिक राशियों लम्बाई, समय, द्रव्यमान, विद्युत धारा, ताप, ज्योति तीव्रता और पदार्थ की मात्रा को ‘मूल राशियाँ’ कहते है।
व्युत्पन्न मात्रक
कुछ अन्य भौतिक राशियों के मात्रक इन सात आधारी मात्रकों से प्राप्त होते हैं और इसलिए इन मात्रकों को ‘व्युत्पन्न मात्रक’ कहते हैं, जैसे क्षेत्रफल का मात्रक वर्गमीटर, घनत्व का मात्रक किलोग्राम प्रति घनमीटर, वेग का मात्रक मीटर प्रति सेकण्ड, बल का मात्रक न्यूटन, कार्य या ऊर्जा का मात्रक जूल, विभवान्तर का मात्रक वोल्ट आदि।
मात्रक पद्धतियां (Systems of Units)
भौतिक राशियों के मापन के लिए निम्न चार पद्धतियां प्रचलित हैं –
1. CGS पद्धति: इस पद्धति में लम्बाई, द्रव्यमान तथा समय के मात्रक क्रमश: सेण्टीमीटर, ग्राम और सेकण्ड होते हैं। इसलिए इसे ‘Centimetre-Gram-Second’ या ‘CGS’ पद्धति कहते हैं।
2. FPS पद्धति: इस पद्धति में लम्बाई, द्रव्यमान और समय के मात्रक क्रमशः फुट, पाउण्ड तथा सेकण्ड होते हैं। इसे ‘ब्रिटिश पद्धति’ भी कहते हैं।
3. MKS पद्धति: इस पद्धति में लम्बाई, द्रव्यमान और समय के मात्रक क्रमश: मीटर, किलोग्राम और सेकण्ड में हैं। यह पद्धति CGS पद्धति का ही एक रूप है। इस पद्धति के मात्रक व्यावहारिक मात्रक (Practical units) होते हैं। अत: पिछले कई दशकों से वैज्ञानिक मापों में इस प्रद्धति का प्रयोग किया जाता रहा
अन्तर्राष्ट्रीय पद्धति अथवा SI: सन् 1967 में ‘अन्तर्राष्ट्रीय माप-तौल’ के महाधिवेशन में SI को स्वीकार किया गया जिसका पूरा नाम System International Unites है। SI में S का अर्थ है System और I का International; अतः ‘SI पद्धति’ के स्थान पर केवल SI लिखा जाता है। आजकल सभी वैज्ञानिक कार्यों में इसी पद्धति का प्रयोग किया जाता है। इस पद्धति में सात मूल मात्रक और दो सम्पूरक मात्रक (Supplementary units) होते हैं। इसका विवरण अग्रलिखित सारणी में दिया गया है।
| भौतिक राशि | मात्रक के नाम | मात्रक के संकेत |
| लम्बाई | मीटर (metre) | .m (मी.) |
| द्रव्यमान | किलोग्राम (kilogram) | kg (किग्रा.) |
| समय | सेकण्ड (second) | s (एस) |
| ताप | केल्विन (kelvin) | K (के) |
| विद्युत धारा | ऐम्पियर (ampere) | A (ऐ) |
| ज्योति-तीव्रता | कैण्डेला (candela) | ed (कैण्ड) |
| पदार्थ के द्रव्य मान | मोल (mole) | mol (मोल) |
SI के सम्पूरक मात्रक
1. रेडियन (Radian): समतल पर बने हुए कोणों को मापने के लिए इस मात्रक का प्रयोग किया जाता है, किसी वृत्त की त्रिज्या के बराबर लम्बाई के चाप द्वारा उसके केन्द्र पर बनाया गया कोण एक रेडियन होता है।
2. स्टेरेडियन (Steradian): यह ठोसीय कोणों (Solid angles) को मापने का मात्रक है।
प्रमुख तथ्य
- भौतिकी में बहुत छोटी और बहुत बड़ी राशियों के मानों को दस की घात के रूप में व्यक्त किया जाता है। उदाहरण के लिए, पृथ्वी और सूर्य के बीच की औसत दूरी 14,950 करोड़ मीटर है। इसे 1.495 x 1011 मीटर लिखना अधिक सुविधाजनक है।
- प्रकाशवर्ष (Light Year): प्रकाशवर्ष दूरी का मात्रक है। एक वर्ष में प्रकाश द्वारा तय की गई दूरी को एक ‘प्रकाशवर्ष’ कहते हैं। 1 प्रकाशवर्ष = 9.46 x 1015 मी.
- ऐम्पियर: यदि दो लम्बे और पतले तारों को निर्वात में 1 मीटर की दूरी एक-दूसरे के समानान्तर रखा जाए और उनमें ऐसे परिमाण की समान विद्युत धारा प्रवाहित की जाए जिससे तारों के बीच प्रति मीटर लम्बाई में 2 x 10-7 न्यूटन का बल लगने लगे, तो विद्युत धारा के परिमाण को 1 ऐम्पियर कहा जाता है।
- ताप का मूल मात्रक केल्विनः जल के त्रिक् बिन्दु (Tripple point) के ऊष्मागतिक ताप के 1/273.16 वें भाग को एक केल्विन कहते हैं। इसका प्रतीक K है। इसके आगे डिग्री नहीं लगाते हैं। उदाहरण के लिए, 10K लिखा जाएगा, 10°K लिखना अब अशुद्ध माना जाता है।
- जल का त्रिक बिन्दु वह ताप है जिस पर बर्फ, जल तथा जलवाष्प तीनों ही तापीय सन्तुलन (Thermal equilibrium) में रहते हैं।
- ज्योति-तीव्रता का मूल मात्रक कैण्डेला: किसी निश्चित दिशा में किसी प्रकाश स्रोत की ज्योति-तीव्रता 1 कैण्डेला तब कही जाती है जब यह स्रोत उस दिशा में 540 x 1012 हर्टज़ आवृत्ति का तथा – वाट स्टेरेडियन तीव्रता का एकवर्णीय (Monochromatic) प्रकाश उत्सर्जित करता है।
- वाट (Watt) शक्ति (Power) का मात्रक है और स्टेरेडियन घन कोण का मात्रक है।
- पदार्थ की मात्रा (Amount of Substance) का मूल मात्रक मोल: यह पदार्थ के परिमाण का मात्रक है, परन्तु ध्यान रहे कि यह द्रव्यमान का मात्रक नहीं है।
| STANDARD METRIC CONVERSIONS | |||||
| 1 inch | = | 2.54 centimeters | 1 in | = | 2.54 cm |
| 1 foot | = | 30.48 centimeters | 1 ft | = | 30.48 cm |
| 1 yard | = | 91.44 centimeters | 1 yd | = | 91.44 cm |
| 1 yard | = | 0.9144 meters | 1 yd | = | 0.9144 m |
| 1 mile | = | 1609.344 meters | 1 mi | = | 1609.344 m |
| 1 mile | = | 1.609344 kilometers | 1 mi | = | 1.609344 km |
| METRIC STANDARD CONVERSIONS | |||||
| 1 millimeter | = | 0.03937 inches | 1 mm | = | 0.03937 in |
| 1 centimeter | = | 0.39370 inches | 1 cm | = | 0.39370 in |
| 1 meter | = | 39.37008 inches | 1 m | = | 39.37008 in |
| 1 meter | = | 3.28084 feet | 1 m | = | 3.28084 ft |
| 1 meter | = | 1.09361 yards | 1 m | = | 1.09361 yd |
| 1 kilometer | = | 1093.6133 yards | 1 km | = | 1093.6133 yd |
| 1 kilometer | = | 0.62137 miles | 1 km | = | 0.62137 mi |
| STANDARD CONVERSIONS | |||||
| 1 foot | = | 12 inches | 1 ft | = | 12 in |
| 1 yard | = | 3 feet | 1 yd | = | 3 ft |
| 1 yard | = | 36 inches | 1 yd | = | 36 in |
| 1 mile | = | 1760 yards | 1 mi | = | 1760 yd |
| METRIC CONVERSIONS | |||||
| 1 centimeter | = | 10 millimeters | 1 cm | = | 10 mm |
| 1 meter | = | 100 centimeters | 1 m | = | 100 cm |
| 1 kilometer | = | 1000 meters | 1 km | = | 1000 m |
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